This document discusses series and parallel combinations of resistors. In a series combination, the same current flows through each resistor. The total resistance is equal to the sum of the individual resistances. In a parallel combination, the same voltage is applied across each resistor. The total resistance is lower than either individual resistance and is calculated using reciprocal sums. Examples of identifying series and parallel combinations in more complex circuits are also provided.
The document discusses electric circuits, including potential difference (p.d.), electromotive force (e.m.f.), internal resistance, and different resistor combinations. It defines p.d. and e.m.f., noting that e.m.f. is the electrical potential energy transferred per coulomb from a source. It explains that internal resistance causes energy loss in a circuit. Resistors can be connected in series or parallel, and formulas are provided for calculating total resistance in each case. Circuit diagrams, ammeters, voltmeters, and potential dividers are also described.
Resistors restrict electric current flow and are commonly used to limit currents. Resistor values are indicated by colored bands according to an international standard code. Standard resistor values are available in preset ranges (E6 or E12 series) that provide sufficient accuracy for most circuits while avoiding impractical intermediate values. Power ratings ensure resistors can safely withstand the heat generated by currents without damage.
In a series circuit, the current is the same at all points but the voltage varies. The total resistance is found by adding the individual resistances. In a parallel circuit, the current varies across branches while the voltage is the same, and total resistance is calculated using reciprocal sums of the individual resistances. A potential divider uses resistors in series to divide an input voltage into fractions at points across the resistors.
Resistance is a property that hinders the flow of electricity and converts it to another form of energy like heat. It is measured in ohms and depends on four factors - the type of material, its cross-sectional area, length, and temperature. Ohm's law states that the voltage between two points is directly proportional to the current flowing through, and resistance can be calculated by dividing the voltage by the current. An ohmmeter is used to measure resistance in a circuit.
Alessandro Volta invented electric battery. It was first named as Voltaic Pile. For his contributions to science, the unit of electric potential is named as Volt. John Frederic Daniell developed Daniell cell. Copy the link given below and paste it in new browser window to get more information on Cells in Series and in Parallel www.askiitians.com/iit-jee-electric-current/cells-in-series-and-in-parallel/
This document discusses resistors in series and parallel circuits. It defines series and parallel circuits, provides diagrams of each, and derives the formulas for calculating equivalent resistance in series (sum of individual resistances) and parallel (reciprocal of the sum of reciprocals of individual resistances) circuits. It concludes by giving examples of applications of resistors in heating elements, lighting, and automotive components.
Series and parallel circuits, venn diagramjohnwest
The document provides instructions for students to compare and contrast a series and parallel circuit by listing their similarities and differences using a Venn diagram. Students are then asked to discuss their findings with peers and check their work against examples on the board. Finally, students must explain the similarities between the circuits in one paragraph and the differences in another paragraph, using provided linking words.
The document discusses two topics:
1) Strain gauges, which measure strain or extension. When a wire in a strain gauge is stretched, its resistance increases due to an increase in length and decrease in cross-sectional area. The change in resistance is directly proportional to the change in length.
2) Light-emitting diodes (LEDs), which emit light when forward biased with current below 20 mA. LEDs can be damaged if reverse biased above 5V. Resistors in series with LEDs limit current to safe levels. LEDs indicate the state of outputs from devices like op-amps by emitting different colors for positive and negative voltages.
The document discusses electric circuits, including potential difference (p.d.), electromotive force (e.m.f.), internal resistance, and different resistor combinations. It defines p.d. and e.m.f., noting that e.m.f. is the electrical potential energy transferred per coulomb from a source. It explains that internal resistance causes energy loss in a circuit. Resistors can be connected in series or parallel, and formulas are provided for calculating total resistance in each case. Circuit diagrams, ammeters, voltmeters, and potential dividers are also described.
Resistors restrict electric current flow and are commonly used to limit currents. Resistor values are indicated by colored bands according to an international standard code. Standard resistor values are available in preset ranges (E6 or E12 series) that provide sufficient accuracy for most circuits while avoiding impractical intermediate values. Power ratings ensure resistors can safely withstand the heat generated by currents without damage.
In a series circuit, the current is the same at all points but the voltage varies. The total resistance is found by adding the individual resistances. In a parallel circuit, the current varies across branches while the voltage is the same, and total resistance is calculated using reciprocal sums of the individual resistances. A potential divider uses resistors in series to divide an input voltage into fractions at points across the resistors.
Resistance is a property that hinders the flow of electricity and converts it to another form of energy like heat. It is measured in ohms and depends on four factors - the type of material, its cross-sectional area, length, and temperature. Ohm's law states that the voltage between two points is directly proportional to the current flowing through, and resistance can be calculated by dividing the voltage by the current. An ohmmeter is used to measure resistance in a circuit.
Alessandro Volta invented electric battery. It was first named as Voltaic Pile. For his contributions to science, the unit of electric potential is named as Volt. John Frederic Daniell developed Daniell cell. Copy the link given below and paste it in new browser window to get more information on Cells in Series and in Parallel www.askiitians.com/iit-jee-electric-current/cells-in-series-and-in-parallel/
This document discusses resistors in series and parallel circuits. It defines series and parallel circuits, provides diagrams of each, and derives the formulas for calculating equivalent resistance in series (sum of individual resistances) and parallel (reciprocal of the sum of reciprocals of individual resistances) circuits. It concludes by giving examples of applications of resistors in heating elements, lighting, and automotive components.
Series and parallel circuits, venn diagramjohnwest
The document provides instructions for students to compare and contrast a series and parallel circuit by listing their similarities and differences using a Venn diagram. Students are then asked to discuss their findings with peers and check their work against examples on the board. Finally, students must explain the similarities between the circuits in one paragraph and the differences in another paragraph, using provided linking words.
The document discusses two topics:
1) Strain gauges, which measure strain or extension. When a wire in a strain gauge is stretched, its resistance increases due to an increase in length and decrease in cross-sectional area. The change in resistance is directly proportional to the change in length.
2) Light-emitting diodes (LEDs), which emit light when forward biased with current below 20 mA. LEDs can be damaged if reverse biased above 5V. Resistors in series with LEDs limit current to safe levels. LEDs indicate the state of outputs from devices like op-amps by emitting different colors for positive and negative voltages.
This document discusses finding the equivalent resistance of a circuit with both series and parallel resistors. It provides the formulas for calculating equivalent resistance of series resistors as the sum of individual resistances, and of parallel resistors as the inverse of the sum of the inverses of individual resistances. The document then works through an example circuit, calculating the equivalent resistances of components in series and parallel and arriving at a final equivalent resistance of 14.44 ohms for the overall circuit.
Series circuits have components connected end to end so the same current passes through each one and the total resistance is the sum of the individual resistances. If one component fails, the entire circuit fails. Parallel circuits have elements connected independently so removing one does not affect the others, and the voltage is the same across each branch while the current divides between the paths.
The document discusses resistors, resistance, and circuits. It covers thermistors and how their resistance changes with temperature. Superconductors and how their resistance drops to zero below a critical temperature is explained. Series and parallel resistor circuits are analyzed. Methods for calculating total resistance, current, and power in circuits are provided along with example problems and their solutions.
This document discusses resistors and resistor combinations in circuits. It covers resistor types including fixed and variable resistors. It also covers resistor color codes and examples of resistors in series and parallel combinations. The key topics are resistances and their combinations in series and parallel and how to calculate equivalent resistances for complex resistor networks using Ohm's law.
Phys 102 formal simple dc circuits lab reportkgreine
In this lab experiment, the student built both series and parallel circuits containing three resistors each to investigate the relationships between resistance, potential difference, and current. For the series circuit, the student found that the current remains the same throughout while the potential difference varies across each resistor. For the parallel circuit, the current varies across each resistor while the potential difference remains the same. The student's measurements matched well with theoretical calculations, validating the circuit concepts.
This lab experiment aims to verify Ohm's law by measuring resistance in series and parallel circuits. Resistors R1 and R2 are connected in different circuits and the current and voltage are measured. The resistance is calculated from Ohm's law and by finding the slope of the I-V graph. The measured resistances are then compared to theoretical values to see if they satisfy Ohm's law for series and parallel circuits. A report is made with the data sheet, graphs, discussion and percentage error calculation.
This document covers combination circuits, which have multiple current paths and resistors that can be in series or parallel. It defines combination circuits and lists the rules for series and parallel circuits. It also provides examples of solving combination circuits by simplifying, reducing, and redrawing equivalent circuits before applying Ohm's law to solve for values.
5.2 - Internal Resistance, Power & Combining Resistorssimonandisa
Internal resistance is the resistance of a battery or cell that causes some of the battery's voltage to be dropped internally rather than available to do work. The voltage available for an external circuit (PD) is less than the battery's open circuit voltage (EMF). Power is the rate at which electrical energy is transferred, calculated as voltage times current, or the current squared times the resistance. Resistors can be combined in series or parallel circuits. Series circuits add the resistances together while parallel circuits decrease the total resistance.
Resistors measurement in series and parallel circuitsAnkur Shrivastava
This document discusses resistors in series and parallel circuits. It explains that to calculate current or voltage, the total resistance must first be determined. For resistors in series, the total resistance is equal to the sum of the individual resistances. For resistors in parallel, the total resistance is calculated by taking the reciprocal of the sum of the reciprocals of the individual resistances, which is always smaller than any single resistance. Sample problems are provided for calculating total resistance and current in both series and parallel circuits.
This document summarizes an experiment conducted by Vania Lundina to verify how the length of a conductor affects its resistance according to Ohm's Law. The experiment involved measuring the resistance of copper wires of varying lengths (10-35 cm) using a voltmeter, ammeter, and power supply. The results showed that resistance increased with increasing length, supporting the conclusion that resistance is directly proportional to length as predicted by Ohm's Law. Some variability between trials was attributed to inaccuracies in measuring wire length.
Resistance is a measure of how much a component resists or reduces the flow of electric current. Components with higher resistance allow less current to flow than those with lower resistance. Resistance is calculated by dividing the voltage by the current using the formula: Resistance (R) = Voltage (V) / Current (I). This relationship can be used to determine the resistance of resistors in circuits based on the voltage provided and current flowing.
This document summarizes an experiment to verify Ohm's law and analyze resistive circuits. The experiment has two parts: 1) Develop a voltage-current characteristic curve for a resistor to verify Ohm's law. Measure voltage and current at increasing voltage levels and plot the relationship. 2) Determine voltages and currents in series and parallel resistor circuits using voltage and current divider rules. Measure voltages across individual resistors in series to verify calculations match measurements.
1. The document describes an experiment to verify Ohm's Law, which states that the current through a conductor is directly proportional to the voltage applied and inversely proportional to the resistance.
2. The experiment involves setting up a circuit with a resistor and voltage source, measuring the current and voltage at different resistances, and showing that a linear relationship exists between current and voltage.
3. The results show that the ratio of voltage to current remains nearly constant at different measurements, and a graph of current versus voltage produces a straight line as expected from Ohm's Law, verifying it experimentally.
The document provides the solution to a physics problem involving two resistors connected in series and parallel configurations. When connected in series, their effective resistance is 3 ohms, and when connected in parallel it is 2/3 ohms. Using these values and equations for series and parallel resistances, the problem determines that the individual resistances of the two resistors are 2 ohms and 1 ohm.
Resistance is a property that restricts electric current flow through a component. The energy from the voltage drives current through the component, appearing as heat. Resistance is measured in ohms, often given in kilo- and mega-ohms for electronics. When resistors are connected in series, their combined resistance equals the sum of individual resistances, while resistors in parallel have lower combined resistance calculated using reciprocal equations. Materials can be conductors, semiconductors, or insulators depending on their resistance properties.
Sample lab-report on verfication of ohms lawminteshat
This laboratory report summarizes an experiment to verify Ohm's Law. The experiment used resistors with values of 1.0kΩ and 1.2kΩ in various circuit configurations. Measurements were made of voltage, current, and resistor values using a digital multimeter. The results closely matched the expected theoretical values based on Ohm's Law. This confirmed that Ohm's Law accurately describes the relationship between voltage, current, and resistance in electrical circuits. The experiment also verified the resistor color code system and that total resistance in a series circuit equals the sum of individual resistances.
1. In a series circuit, the same current flows through each component and there is only one path for electricity to flow.
2. The total resistance of a series circuit equals the sum of the individual resistances.
3. The voltage applied to a series circuit equals the sum of the individual voltage drops across each component. If any one component fails or is disconnected, no current will flow through the entire circuit.
This document discusses methods for determining the shape of a resistor grid given boundary measurements. It presents the basic problem of inferring the height of each column from voltage and current measurements on the front nodes. An algorithm is proposed that propagates this data inward row-by-row, setting nodes to 0 when their voltage becomes negative. However, the method is highly unstable to errors due to amplification during propagation. Short, squat grids can be recovered more accurately than tall grids with many propagation steps. Regulation is needed to limit error growth from the propagation matrix's large eigenvalues.
1. The document discusses various radiation measurement devices and apps for measuring radiation on iPhone and Android phones including the GM-01A, GM-01B, and GAMoV app.
2. It provides background radiation levels and measurements in CPM and μSV/h from various Geiger counters like the SBM-20, SI-1G, and others at different locations.
3. Links are provided for downloading the GAMoV Android and iPhone apps as well as websites with more information on radiation measurement and different Geiger counter devices.
This document outlines a lesson plan for teaching capacitors in series and parallel. It includes the learning objectives, which are to describe how a capacitor works, calculate charging time, distinguish between series and parallel circuits, and explain capacitor charge and discharge. The lesson plan consists of an opening activity, lecture and examples on capacitor charging, worksheets for practice, a demonstration experiment, explanation of series and parallel capacitor circuits, and a closing reflection. Formal lesson plan requirements such as page layout and numbering are also specified.
This document discusses finding the equivalent resistance of a circuit with both series and parallel resistors. It provides the formulas for calculating equivalent resistance of series resistors as the sum of individual resistances, and of parallel resistors as the inverse of the sum of the inverses of individual resistances. The document then works through an example circuit, calculating the equivalent resistances of components in series and parallel and arriving at a final equivalent resistance of 14.44 ohms for the overall circuit.
Series circuits have components connected end to end so the same current passes through each one and the total resistance is the sum of the individual resistances. If one component fails, the entire circuit fails. Parallel circuits have elements connected independently so removing one does not affect the others, and the voltage is the same across each branch while the current divides between the paths.
The document discusses resistors, resistance, and circuits. It covers thermistors and how their resistance changes with temperature. Superconductors and how their resistance drops to zero below a critical temperature is explained. Series and parallel resistor circuits are analyzed. Methods for calculating total resistance, current, and power in circuits are provided along with example problems and their solutions.
This document discusses resistors and resistor combinations in circuits. It covers resistor types including fixed and variable resistors. It also covers resistor color codes and examples of resistors in series and parallel combinations. The key topics are resistances and their combinations in series and parallel and how to calculate equivalent resistances for complex resistor networks using Ohm's law.
Phys 102 formal simple dc circuits lab reportkgreine
In this lab experiment, the student built both series and parallel circuits containing three resistors each to investigate the relationships between resistance, potential difference, and current. For the series circuit, the student found that the current remains the same throughout while the potential difference varies across each resistor. For the parallel circuit, the current varies across each resistor while the potential difference remains the same. The student's measurements matched well with theoretical calculations, validating the circuit concepts.
This lab experiment aims to verify Ohm's law by measuring resistance in series and parallel circuits. Resistors R1 and R2 are connected in different circuits and the current and voltage are measured. The resistance is calculated from Ohm's law and by finding the slope of the I-V graph. The measured resistances are then compared to theoretical values to see if they satisfy Ohm's law for series and parallel circuits. A report is made with the data sheet, graphs, discussion and percentage error calculation.
This document covers combination circuits, which have multiple current paths and resistors that can be in series or parallel. It defines combination circuits and lists the rules for series and parallel circuits. It also provides examples of solving combination circuits by simplifying, reducing, and redrawing equivalent circuits before applying Ohm's law to solve for values.
5.2 - Internal Resistance, Power & Combining Resistorssimonandisa
Internal resistance is the resistance of a battery or cell that causes some of the battery's voltage to be dropped internally rather than available to do work. The voltage available for an external circuit (PD) is less than the battery's open circuit voltage (EMF). Power is the rate at which electrical energy is transferred, calculated as voltage times current, or the current squared times the resistance. Resistors can be combined in series or parallel circuits. Series circuits add the resistances together while parallel circuits decrease the total resistance.
Resistors measurement in series and parallel circuitsAnkur Shrivastava
This document discusses resistors in series and parallel circuits. It explains that to calculate current or voltage, the total resistance must first be determined. For resistors in series, the total resistance is equal to the sum of the individual resistances. For resistors in parallel, the total resistance is calculated by taking the reciprocal of the sum of the reciprocals of the individual resistances, which is always smaller than any single resistance. Sample problems are provided for calculating total resistance and current in both series and parallel circuits.
This document summarizes an experiment conducted by Vania Lundina to verify how the length of a conductor affects its resistance according to Ohm's Law. The experiment involved measuring the resistance of copper wires of varying lengths (10-35 cm) using a voltmeter, ammeter, and power supply. The results showed that resistance increased with increasing length, supporting the conclusion that resistance is directly proportional to length as predicted by Ohm's Law. Some variability between trials was attributed to inaccuracies in measuring wire length.
Resistance is a measure of how much a component resists or reduces the flow of electric current. Components with higher resistance allow less current to flow than those with lower resistance. Resistance is calculated by dividing the voltage by the current using the formula: Resistance (R) = Voltage (V) / Current (I). This relationship can be used to determine the resistance of resistors in circuits based on the voltage provided and current flowing.
This document summarizes an experiment to verify Ohm's law and analyze resistive circuits. The experiment has two parts: 1) Develop a voltage-current characteristic curve for a resistor to verify Ohm's law. Measure voltage and current at increasing voltage levels and plot the relationship. 2) Determine voltages and currents in series and parallel resistor circuits using voltage and current divider rules. Measure voltages across individual resistors in series to verify calculations match measurements.
1. The document describes an experiment to verify Ohm's Law, which states that the current through a conductor is directly proportional to the voltage applied and inversely proportional to the resistance.
2. The experiment involves setting up a circuit with a resistor and voltage source, measuring the current and voltage at different resistances, and showing that a linear relationship exists between current and voltage.
3. The results show that the ratio of voltage to current remains nearly constant at different measurements, and a graph of current versus voltage produces a straight line as expected from Ohm's Law, verifying it experimentally.
The document provides the solution to a physics problem involving two resistors connected in series and parallel configurations. When connected in series, their effective resistance is 3 ohms, and when connected in parallel it is 2/3 ohms. Using these values and equations for series and parallel resistances, the problem determines that the individual resistances of the two resistors are 2 ohms and 1 ohm.
Resistance is a property that restricts electric current flow through a component. The energy from the voltage drives current through the component, appearing as heat. Resistance is measured in ohms, often given in kilo- and mega-ohms for electronics. When resistors are connected in series, their combined resistance equals the sum of individual resistances, while resistors in parallel have lower combined resistance calculated using reciprocal equations. Materials can be conductors, semiconductors, or insulators depending on their resistance properties.
Sample lab-report on verfication of ohms lawminteshat
This laboratory report summarizes an experiment to verify Ohm's Law. The experiment used resistors with values of 1.0kΩ and 1.2kΩ in various circuit configurations. Measurements were made of voltage, current, and resistor values using a digital multimeter. The results closely matched the expected theoretical values based on Ohm's Law. This confirmed that Ohm's Law accurately describes the relationship between voltage, current, and resistance in electrical circuits. The experiment also verified the resistor color code system and that total resistance in a series circuit equals the sum of individual resistances.
1. In a series circuit, the same current flows through each component and there is only one path for electricity to flow.
2. The total resistance of a series circuit equals the sum of the individual resistances.
3. The voltage applied to a series circuit equals the sum of the individual voltage drops across each component. If any one component fails or is disconnected, no current will flow through the entire circuit.
This document discusses methods for determining the shape of a resistor grid given boundary measurements. It presents the basic problem of inferring the height of each column from voltage and current measurements on the front nodes. An algorithm is proposed that propagates this data inward row-by-row, setting nodes to 0 when their voltage becomes negative. However, the method is highly unstable to errors due to amplification during propagation. Short, squat grids can be recovered more accurately than tall grids with many propagation steps. Regulation is needed to limit error growth from the propagation matrix's large eigenvalues.
1. The document discusses various radiation measurement devices and apps for measuring radiation on iPhone and Android phones including the GM-01A, GM-01B, and GAMoV app.
2. It provides background radiation levels and measurements in CPM and μSV/h from various Geiger counters like the SBM-20, SI-1G, and others at different locations.
3. Links are provided for downloading the GAMoV Android and iPhone apps as well as websites with more information on radiation measurement and different Geiger counter devices.
This document outlines a lesson plan for teaching capacitors in series and parallel. It includes the learning objectives, which are to describe how a capacitor works, calculate charging time, distinguish between series and parallel circuits, and explain capacitor charge and discharge. The lesson plan consists of an opening activity, lecture and examples on capacitor charging, worksheets for practice, a demonstration experiment, explanation of series and parallel capacitor circuits, and a closing reflection. Formal lesson plan requirements such as page layout and numbering are also specified.
series and parallel connection of capacitor2461998
This document discusses the series and parallel connections of capacitors. It provides the following key points:
- Capacitors in series have the same charge but their voltages add up. The equivalent capacitance is calculated by taking the reciprocal of the sum of the reciprocals of the individual capacitances.
- Capacitors in parallel have the same voltage but their charges add up. The equivalent capacitance is calculated by summing the individual capacitances.
- Complex circuits can be reduced to equivalent series or parallel combinations by applying these rules repeatedly until the full equivalent capacitance can be determined.
The Wilson cloud chamber was invented in 1911 by Charles Thomson Rees Wilson to observe the paths of ionizing particles like alpha, beta, and gamma radiation. It consists of a closed chamber with a glass top and a movable piston bottom, and contains alcohol vapor that becomes supersaturated when the piston is rapidly pulled down. When ionizing particles pass through, they leave ions that cause droplets to form along the particle's path, allowing the path to be detected and photographed. An electric field can then sweep out the ions to prepare the chamber for future use.
This document discusses the combination of resistors in series and parallel circuits and how to calculate the total resistance. It provides the equations for calculating total resistance for resistors in series (Rtotal = R1 + R2) and parallel (1/Rtotal = 1/R1 + 1/R2). Several example calculations are shown applying these equations to circuits with 2-3 resistors in both series and parallel combinations.
Nuclear fusion is a nuclear reaction where two atomic nuclei collide and join to form a new nucleus. This occurs at very high speeds and temperatures, as the positive charges of the nuclei repel each other. During fusion, a small amount of mass is converted to energy. Fusion powers stars and is responsible for the creation of elements in the universe. Achieving controlled fusion on Earth could lead to a virtually limitless source of energy but has proven extremely difficult to realize.
This is the seminar report on the topic Nuclear fusion and its prospects as a future source of Energy. You can also look for the slides that I've published by the same title.
1) Boosted fission weapons use small amounts of deuterium and tritium gas in the core of a fission bomb, producing a faster fission reaction that increases energy yield over 200% compared to regular fission.
2) Staged radiation implosion, or Teller-Ulam, weapons are two-stage processes using lighter fusion elements after a fission trigger, releasing more energy from the separate fusion reaction and subsequent fast fissioning of materials.
3) The "alarm clock" or "sloika" design uses concentric uranium or plutonium shells, but fusion is only 15-20% of yield, making it inefficient compared to staged designs. The
The document discusses nuclear fission and fusion. Nuclear fission occurs when a nucleus splits into two smaller nuclei and releases neutrons. There are two types of fission: spontaneous fission of unstable radioactive isotopes and induced fission which is caused by bombarding atoms with neutrons. Nuclear fusion occurs when two low mass nuclei combine to form a higher mass nucleus and release energy. Fusion takes place in stars and involves hydrogen fusing to form helium.
This document discusses different types of solid state radiation detectors, including scintillation detectors, thermoluminescent dosimeters (TLD), and semiconductor detectors. Scintillation detectors detect radiation via light emission in inorganic crystal materials like NaI or organic crystals like anthracene. TLDs "capture" radiation dose information and release light when heated, allowing dose measurement. Common TLD materials are LiF:Mg,Ti and Li2B4O7:Mn. Semiconductor detectors like silicon and germanium act as solid state ionization chambers and are used for high resolution energy measurement of alpha and beta particles.
Nuclear fusion is the process of forcing together atomic nuclei to produce energy and involves using extremely high temperatures over 100 million Kelvin to fuse hydrogen atoms together. Successful nuclear fusion requires achieving and maintaining high plasma density and confinement through magnetic fields to contain the hot plasma long enough for fusion reactions to occur at significant rates and has been achieved at experimental facilities like JET in the UK and JT60 in Japan which have produced over 16 megawatts and 5.4 megawatts respectively through magnetic confinement fusion since the 1980s.
This document provides information on nuclear fission and fusion. It defines fission as the splitting of an atomic nucleus when bombarded by neutrons, which releases energy. Fusion is defined as the joining of atomic nuclei to form heavier nuclei with the release of energy. The document discusses the history of fission's discovery and the processes of fission and fusion in detail through diagrams and explanations. It also addresses differences between fission and fusion such as the energy released and temperatures required for the reactions.
Geiger–Müller Counter is a hand-held radiation survey instrument used in Radiation Dosimetry,Nuclear Physics,Experimental Physics & Radiological Protection.
Nuclear fusion involves fusing together light atomic nuclei such as hydrogen isotopes deuterium and tritium to release energy. It requires extremely high temperatures to fuse atomic nuclei together, which plasma confinement techniques aim to achieve. Fusion promises a virtually limitless and carbon-free source of energy, but producing self-sustaining fusion reactions requires solving significant technical challenges and has yet to be achieved on a commercial scale.
The Joint European Torus (JET) nuclear fusion research plant located at a retired navy airfield in the UK was constructed in 1983 but faced power issues as the tokamak reactor required too much electricity from the main grid. This was solved by adding two large flywheel generators to provide the necessary power. JET was originally run by Euratom but was later taken over by the UK Atomic Energy Authority in 1999. It underwent upgrades from 2009-2012 before resuming operations, and achieved a fusion energy gain factor of 0.7. JET continues to be an important facility for nuclear fusion research.
Radiation detection devices are instruments that can identify the presence of radiation in the environment, on surfaces, inside or outside of people. Some common radiation detection devices include Geiger Mueller detectors with pancake probes, which detect and measure radiation in real time, alpha radiation survey meters for detecting alpha radiation, and dose rate meters that measure environmental radiation levels and determine safety. Personal dosimeters are worn to monitor radiation exposure, while newer devices can identify isotopes, measure dose and dose rate, and monitor multiple contamination types.
This document discusses various methods for detecting radiation. It outlines passive detectors like photographic film, electroscopes, dosimeters, and thermoluminescent dosimeters (TLDs) which do not require a power source. Active detectors mentioned include Geiger-Muller tubes and scintillation detectors, which need a constant energy supply. Both types detect radiation indirectly by ionizing matter and detecting the ions produced, though active detectors provide more information about the radiation type and energy.
A Geiger-Muller counter consists of a gas-filled tube that detects ionizing radiation such as alpha particles, beta particles, and gamma rays. When radiation enters the tube, it ionizes the gas and produces a pulse of current that is counted by a scaler. To prevent additional pulses from a single radiation event, a small amount of quenching gas is added which absorbs excess energy and prevents further ionization of the main gas. The Geiger-Muller counter has a dead time after each detection where it cannot detect additional radiation as it re-establishes the electric field inside the tube.
This document discusses types of radiation, their interaction with matter, and radiation detectors. It covers the following types of radiation: photons (gamma rays and x-rays), neutrons, electrons, ions, protons, and alpha particles. It describes the processes of photoelectric effect, Compton scattering, and pair production for photon interaction, as well as scattering, capture and other interactions for neutrons. The document also discusses why radiation detection is important and gives examples of different types of radiation detectors like gas detectors, scintillation detectors, and semiconductor detectors.
The document summarizes the Geiger-Müller counter, an instrument used to detect ionizing radiation such as alpha particles, beta particles, and gamma rays. It describes the history and development of the counter, from its original detection principle discovered in 1908 to its modern form using a Geiger-Müller tube. The operating principle is explained, where ionization events in an inert gas-filled tube produce electrical pulses that are counted and displayed. Different readout types including counts per second and absorbed dose are discussed. Applications include detection of radioactive materials and environmental monitoring for radiation levels.
Resistors can be connected in series, parallel, or a combination of both. In series, the total resistance is the sum of individual resistances. In parallel, the total resistance is lower than the lowest individual resistance. Complex circuits can be reduced to an equivalent single resistance by repeatedly replacing series or parallel sections with equivalent components. This allows complicated circuits to be analyzed easily using Ohm's law.
Sheet1ResistorcolorResistance (kohms)40 ohm resistor39.94 ohm1brown black yellow silver1322red1823brown green orange13.34brown gray orange gold18.35green1836blue black red gold60.67orange blue orange gold34.4k ohmsmeasured resistanceSeries Circuit1,2,5497.498Mohms3,4,76666Kohms1,6,5375.6.377Mohms7,3,4,2248248KohmsK ohms TheoreticalParallel1,2,553.95543,4,76.2936.31,5,633.8533.92,3,4,76.086.09HybridK ohms TheoreticalK ohms observed1 in series 2 and 5 in parallel223.2223.93 in series and 4 and 7 in parallel25.225.21 in series and 6 and 5 in parallel177.5178
Sheet2Characteristic CurvemVmALight bulb3.83.336.933.861.75590.377118951521131901292491463501635501819522091440228153023425702844070345-0.05-0.056-6.51-5.98-13.2-12.1-25.8-23.7-54.4-48.9-95.5-80.6-126-101-395-168-327-159-211-134-784-195-531-178-1570-236-2500-281-4060-345
3.8 36.9 61.7 90.3 118 152 190 249 350 550 952 1440 1530 2570 4070 -0.05 -6.51 -13.2 -25.8 -54.4 -95.5 -126 -395 -327 -211 -784 -531 -1570 -2500 -4060 3.3 33.799999999999997 55 77 95 113 129 146 163 181 209 228 234 284 345 -5.6000000000000001E-2 -5.98 -12.1 -23.7 -48.9 -80.599999999999994 -101 -168 -159 -134 -195 -178 -236 -281 -345
Sheet3Characteristic CurvemVmADiode2.330.032.930.0370.0370016732307443976867.77931218142008302918444263.160.034.540.0324.40.03700.031860.032700.045821.156172.396504.86666.844320.06-2.340.02-260.02-320.03-9900.04
2.33 2.93 7 700 732 744 768 793 814 830 844 3.16 4.54 24.4 70 186 270 582 617 650 666 432 -2.34 -26 -32 -990 0.03 0.03 0.03 16 30 39 67.7 121 200 291 426 0.03 0.03 0.03 0.03 0.03 0.04 1.1499999999999999 2.39 4.8 6.84 0.06 0.02 0.02 0.03 0.04
Sheet5Characteristic CurveResistormVmA132k ohms2.28-0.00131-0.00115602320.0015300.0037220.00411110.00719900.01423600.01752000.03965400.04994300.071178000.135-2.32-0.001-33-0.001-283-0.003-1120-0.01-1850-0.015-3040-0.024-6940-0.054-10500-0.082-17800-0.138
2.2799999999999998 31 156 232 530 722 1111 1990 2360 5200 6540 9430 17800 -2.3199999999999998 -33 -283 -1120 -1850 -3040 -6940 -10500 -17800 -1E-3 -1E-3 0 1E-3 3.0000000000000001E-3 4.0000000000000001E-3 7.0000000000000001E-3 1.4E-2 1.7000000000000001E-2 3.9E-2 4.9000000000000002E-2 7.0999999999999994E-2 0.13500000000000001 -1E-3 -1E-3 -3.0000000000000001E-3 -0.01 -1.4999999999999999E-2 -2.4E-2 -5.3999999999999999E-2 -8.2000000000000003E-2 -0.13800000000000001
Resistor Circuits and Characteristic Curves
Purpose: In this lab we will introduce basic circuit analysis with series and parallel resistor circuits using Ohms Law and Kirchhoff’s laws. We will also introduce characteristic curves and diodes.
Introduction: Ohm’s Law is of general use with circuit elements, with parts of circuits, or with whole circuits. The voltage across a circuit element is equal to the resistance (or equivalent resistance) times the current flowing through the element. (V=IR)
Kirchhoff’s 1st Law of Circuits: The sum of voltages around a closed loop is equal to zero.
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Household circuits are typically wired in parallel. This has several advantages:
- If one outlet or fixture fails, it does not disable the entire circuit. This is safer and more reliable than series wiring.
- The current drawn by each device is the same as the current supplied by the circuit. In parallel wiring, adding or removing a device does not change the current to the other devices on the circuit. In series, the current must pass through each device in order.
- Parallel wiring allows each outlet or fixture to receive the full voltage supplied by the circuit. In series wiring, the voltage would decrease across multiple components.
The main disadvantage of series wiring a household circuit would be that a failure of any one component would
This document discusses resistors in series connections. It defines a series connection as resistors joined end to end so that the same current flows through each resistor. The total resistance of resistors in series is calculated by adding the individual resistances. Examples of series connections include light switches and Christmas lights. Advantages are simpler construction compared to parallel circuits, but problems include any single resistor failure causing the whole circuit to fail and uneven current draw lowering efficiency. A sample calculation finds the total resistance and current for a series circuit with three specified resistors and a given voltage.
This document discusses resistors in series connections. It defines a series connection as resistors joined end to end so that the same current flows through each resistor. The total resistance of resistors in series is calculated by adding the individual resistances. Examples of series connections include light switches and Christmas lights. Advantages are simpler construction compared to parallel circuits, but problems include any single resistor failure causing the whole circuit to fail and uneven current draw lowering efficiency. A sample calculation finds the total resistance and current for a series circuit with three specified resistors and a given voltage.
Name __________________________________ VannaJoy20
This document describes an experiment investigating the laws of refraction using a simulation. Students will explore how the angle of refraction changes when light passes from air to water and vice versa. They will verify Snell's law, which relates the indices of refraction and angles of incidence and refraction. Students will also use Snell's law to calculate angles of refraction for different materials and scenarios, and check their calculations against the simulation results.
1. The document discusses series circuits and how voltage is divided among resistors in series. It explains that the total resistance of resistors in series is equal to the sum of the individual resistances.
2. A key concept covered is the voltage divider rule - the voltage across each resistor in a series circuit is directly proportional to the ratio of its resistance to the total resistance.
3. Applications of voltage dividers include using potentiometers (variable resistors) to obtain a variable output voltage from a fixed voltage source.
This document provides information about electricity and magnetism, specifically resistance and heating effects of currents. It explains that resistance depends on the material and cross-sectional area of a conductor. It also describes Ohm's law, which states that current is directly proportional to voltage in a conductor. Resistors can be made of nichrome wire or ceramic and carbon. Kirchhoff's laws are introduced to help solve circuit problems using conservation of charge and energy.
The document discusses electricity and magnetism, specifically resistance and heating effects of currents. It explains that resistance depends on the material and structure of a conductor, with tungsten filament lamps having high resistance and copper wires having low resistance. It also covers Ohm's law, defining resistance as the ratio of potential difference to current, and how resistors, circuits, and resistor combinations work based on this relationship. Kirchhoff's laws for analyzing electric circuits are also summarized.
The document outlines a route map for a 12 lesson course on electric circuits. It will cover topics like static electricity, electric charge, circuits, current, resistance, resistors, voltage, power, and electricity generation and distribution. It provides learning objectives and a sample activity for the first lesson which involves drawing a series circuit with batteries, a switch, light bulb, resistor and variable resistor and adding a voltmeter and ammeter.
The document discusses using equivalent resistance to simplify complex resistor networks into a single equivalent resistance. It provides formulas for calculating equivalent resistance of series and parallel resistor combinations. For a sample circuit, it shows how to break the circuit into simpler series and parallel pieces, calculate the equivalent resistance of each piece, and combine them to find the overall equivalent resistance of the full network. This allows determining values like source current and power without solving a complex set of equations.
This document discusses electrical power and energy. It defines electrical power as the rate at which energy is expended or delivered, calculated as voltage times current (P=VI). It explains that power can be calculated for any electrical device where voltage and current are defined. Resistors are used as an example device, where the power dissipated is equal to the voltage across the resistor squared divided by the resistance (P=V^2/R), or the current through the resistor squared times the resistance (P=I^2R). The document poses two sample problems calculating power and resistance.
This document provides an introduction to electricity and electronics. It discusses key concepts like electrons, charge, current, and circuits. It explains that electricity is the movement of electrons in a circuit, and defines common units like the coulomb, ampere, and volt. The document also introduces circuit components like resistors, switches, and batteries. It explains Ohm's law and the relationship between current, voltage, and resistance in circuits. Students are provided examples to calculate values in circuits and learn how changing resistance impacts current.
AP Ch 18 Basic Electric Currents-Teacher.pptMdSazibMollik
This document provides an overview of Chapter 18 from an AP Physics textbook. It covers basic electric circuits including resistances in series and parallel, Kirchhoff's rules for analyzing multi-loop circuits, and how to use ammeters and voltmeters. Homework problems are assigned from pages 592-596 of the textbook.
Liner Resistive networks for electrical engineerscbcbgdfgsdf
This chapter discusses linear resistive networks and their analysis. It covers key topics like resistance, basic network configurations including series and parallel resistors, superposition, and equivalent circuits. Methods like Kirchhoff's laws, Ohm's law, and the concepts of equivalent resistance are presented to analyze resistive circuits containing multiple elements and energy sources. Superposition is introduced as a technique to solve for unknowns in linear circuits with multiple independent sources by considering each source individually.
This document provides an overview of electrical circuits. It defines key concepts like current, voltage, resistance, and capacitance. It explains how circuits work and how to measure current and voltage. It describes the basic components of circuits including cells, lamps, switches, and wires. It also covers circuit diagrams and the two types of circuits: series and parallel. Formulas are provided for calculating equivalent resistance and capacitance for combinations of components.
This document provides an introduction to electricity and electronics. It includes definitions of key concepts like electrons, conductors, insulators, charge and current. It discusses the structure of atoms and how electricity is the movement of electrons through circuits. It explains concepts such as voltage, potential difference, Ohm's law and different types of circuits including series and parallel circuits. Examples and activities are provided to help understand these concepts through building sample circuits and observing current.
This document provides information about electricity and magnetism concepts related to physics achievement standard 2.6. It defines key terms like current, voltage, resistance, and power. It explains physical relationships like Ohm's law. It also describes common circuit components like batteries, resistors, switches, and how components are arranged in series and parallel circuits. Magnetic concepts like the force on a current-carrying wire in a magnetic field are also covered.
This document provides an overview of electricity and circuits that will be covered in unit 2. It includes definitions of key concepts like potential difference, voltage, and circuits. Students will learn about series and parallel circuits, and how to measure current and voltage. They will learn circuit symbols and how to draw circuit diagrams. The goal is for students to understand electricity, circuits, and be able to apply concepts like Ohm's Law by the end of the unit.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
The chapter Lifelines of National Economy in Class 10 Geography focuses on the various modes of transportation and communication that play a vital role in the economic development of a country. These lifelines are crucial for the movement of goods, services, and people, thereby connecting different regions and promoting economic activities.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
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Walmart Business+ and Spark Good for Nonprofits.pdf
Combinations of resistors
1. Combinations of Resistors
Resistors do not occur in isolation. They are almost always part of a
larger circuit, and frequently that larger circuit contains many resistors.
It is often the case that resistors occur in combinations that repeat.
Combinations of Resistors
In this lesson we will look at two recurring resistor combinations,
series combinations and parallel combinations. Those are common
combinations, not only for resistors but other elements as well. (For
example, we can speak of "a resistor in series with a capacitor".)
We'll start by examining series and parallel combinations and then
move on to identifying those combinations when they are "buried" within a
larger circuit. What we're doing is learning how to recognize small
portions of larger circuits. Experts do that. You can click here to see
how experts are able to recognize larger combinations in many situations.
It is a part of the basic "tool box" that an expert in an area acquires as
s/he becomes an expert.
Series Combinations of Resistors
Two elements are said to be in series whenever the same current
physically flows through both of the elements. The critical point is that
the same current flows through both resistors when two are in series.
The particular configuration does not matter. The only thing that
matters is that exactly the same current flows through both resistors.
Current flows into one element, through the element, out of the element
into the other element, through the second element and out of the second
element. No part of the current that flows through one resistor
"escapes" and none is added. This figure shows several different ways
that two resistors in series might appear as part of a larger circuit
diagram.
2. Questions
Here is a circuit you may have seen before. Answer the questions
below for this circuit.
Q1. Are elements #3 and #4 in series?
Q2. Are elements #1 and #2 in series?
Q3. Is the battery in series with any element?
3. You might wonder just how often you actually find resistors in
series. The answer is that you find resistors in series all the time.
An example of series resistors is in house
wiring. The leads from the service entrance
enter a distribution box, and then wires are
strung throughout the house. The current flows
out of the distribution box, through one of the
wires, then perhaps through a light bulb, back
through the other wire. We might model that
situation with the circuit diagram shown below.
In many electronic circuits series resistors are used to get a
different voltage across one of the resistors. We'll look at those
circuits, called voltage dividers, in a short while. Here's the circuit
diagram for a voltage divider.
4. Besides resistors in series, we can also have other elements in series
- capacitors, inductors, diodes. These elements can be in series with
other elements. For example, the simplest form of filter, for filtering
low frequency noise out of a signal, can be built just by putting a resistor
in series with a capacitor, and taking the output as the capacitor voltage.
As we go along you'll have lots of opportunity to use and to expand
what you learn about series combinations as you study resistors in series.
Let's look at the model
again. We see that the wires
are actually small resistors
(small value of resistance,
not necessarily physically
small) in series with the light
bulb, which is also a resistor. We have three resistors in series although
two of the resistors are small. We know that the resistors are in series
because all of the current that flows out of the distribution box through
the first wire also flows through the light bulb and back through the
second wire, thus meeting our condition for a series connection. Trace
that out in the circuit diagram and the pictorial representation above.
Let us consider the simplest case of a series resistor connection,
the case of just two resistors in series. We can perform a thought
experiment on these two resistors. Here is the circuit diagram for the
situation we're interested in.
Imagine that they are embedded in an opaque piece of plastic, so
that we only have access to the two nodes at the ends of the series
connection, and the middle node is inaccessible. If we measured the
resistance of the combination, what would we find? To answer that
question we need to define voltage and current variables for the
5. resistors. If we take advantage of the fact that the current through
them is the same (Apply KCL at the interior node if you are unconvinced!)
then we have the situation below.
Note that we have defined a voltage across each resistor (Va and Vb) and
current that flows through both resistors (Is) and a voltage variable, Vs,
for the voltage that appears across the series combination.
Let's list what we know.
The current through the two resistors is the same.
The voltage across the series combination is given by:
o Vs= Va + Vb
The voltages across the two resistors are given by Ohm's Law:
o Va = Is Ra
o Vb = Is Rb
We can combine all of these relations, and when we do that we find
the following.
Vs= Va + Vb
Vs= Is Ra + Is Rb
Vs= Is (Ra + Rb)
Vs= Is Rseries
Here, we take Rseries to be the series equivalent of the two resistors in
series, and the expression for Rseries is:
Rseries = Ra + Rb
What do we mean by series equivalent? Here are some points to
observe.
6. If current and voltage are proportional, then the device is a
resistor.
We have shown thatVs= Is Rseries, so that voltage is proportional to
current, and the constant of proportionality is a resistance.
We will call that the equivalent series resistance.
There is also a mental picture to use when considering equivalent series
resistance. Imagine that you have two globs of black plastic. Each of the
globs of black plasic has two wires coming out. Inside these two black
plastic globs you have the following.
In the first glob you have two resistors in series. Only the leads of
the series combination are available for measurement externally.
You have no way to penetrate the box and measure things at the
interior node.
In the second box you have a single resistor that is equal to the
series equivalent. Only the leads of this resistor are available for
measurement externally.
Then, if you measured the resistance using the two available leads in the
two different cases you would not be able to tell which black plastic glob
had the single resistor and which one had the series combination.
Here are two resistors. At the top are two 2000W resistors. At
the bottom is single 4000W resistors. (Note, these are not exactly
standard sizes so it took a lot of hunting to find a supply store that sold
them!). You can click the green button to grow blobs around them.
7. After you have grown the blobs around the resistors there is no
electrical measurement you can make that will allow you to tell which one
has two resistors and which one has one resistor. They are electrically
indistinguishable! (Or, in other words, they are equivalent!)
Question
Q4. Is the series equivalent resistor larger than either resistor, or is it
smaller?
Problems
P1. What is the series equivalent of two 1000 resistors in series?
Enter your answer in the box below, then click the button to submit your
answer. You will get a grade on a 0 (completely wrong) to 100 (perfectly
accurate answer) scale.
Your grade is:
P2. What is the series equivalent of a 1000 resistor and a
2700 resistor in series?
8. Your grade is:
P3. What is the series equivalent of three 1000 resistors in series?
You may want to do this problem in two steps.
Your grade is:
P4. Imagine that you have a 100 resistor. You want to add a resistor
in series with this 100 resistor in order to limit the current to 0.5 amps
when 110 volts is placed across the two resistors in series. How much
resistance should you use?
Your grade is:
Parallel Resistors
The other common connection is two elements in parallel. Two
resistors or any two devices are said to be in parallel when the same
voltage physically appears across the two resistors. Schematically, the
situation is as shown below.
Note that we have defined the voltage across both resistor (Vp) and the
current that flows through each resistor (Ia and Ib) and a voltage
variable, Vp, for the voltage that appears across the parallel combination.
9. Let's list what we know.
The voltage across the two resistors is the same.
The current through the parallel combination is given by:
o Ip= Ia + Ib
The currents through the two resistors are given by Ohm's Law:
o Ia = Vp /Ra
o Ib = Vp /Rb
We can combine all of these relations, and when we do that we find
the following.
Ip= Ia + Ib
Ip= Vp /Ra + Vp /Rb
Ip= Vp[ 1/Ra + 1/Rb]
Ip= Vp/Rparallel
Here, we take Rparallel to be the parallel equivalent of the two resistors in
parallel, and the expression for Rparallel is:
1/Rparallel = 1/Ra + 1/Rb
There may be times when it is better to rearrange the expression
for Rparallel. The expression can be rearranged to get:
Rparallel = (Ra*Rb)/(Ra + Rb)
Either of these expressions could be used to compute a parallel
equivalent resistance. The first has a certain symmetry with the
expression for a series equivalent resistance.
Question
Q5 Is the parallel equivalent resistor larger than either resistor, or
is it smaller?
10. Problems
P5. What is the parallel equivalent of two 1000 resistors in parallel?
Enter your answer in the box below, then click the button to submit your
answer. You will get a grade on a 0 (completely wrong) to 100 (perfectly
accurate answer) scale.
Your grade is:
P6. What is the parallel equivalent of a 1000 resistor and a
1500 resistor in parallel?
Your grade is:
P7. What is the equivalent of three 1000 resistors in parallel? You
may want to do this problem in two steps.
Your grade is:
Parallel Resistors - A Point to Remember
It is important to note that the equivalent resistance of two
resistors in parallel is always smaller than either of the two
resistors.
Problems
P8. What is the equivalent resistance of this resistance combination?
11. Your grade is:
P9. What is the equivalent resistance of this resistance combination?
Your grade is:
P10. What is the equivalent resistance of this resistance combination?
Here all three resistors are 33 k . Remember to input your answer in
ohms.
Your grade is:
P11. Here is an operational amplifier circut, a Wien-bridge oscillator.
The circuit is taken from Wojslaw and Moustakas' book Operational
Amplifiers (John Wiley & Sons, 1986, p100). Assuming that the
12. amplifiers take no current at the "+" and "-" terminals are resistors,
R3 and R4 in series?
What If You Have A More Complex Circuit
Here's a circuit with resistors that has them connected in a
different way. For a short while we're going to work on the question of
how to analyze this circuit. For a start we're going to assume that this is
a resistor. It has two leads at the left (marked here with red dots) and
we'll assume that we want to find the equivalent resistance you would
have at those leads.
We will use the following numerical values for the resistors in this
example, and we will work through using these values.
Ra = 1500
Rb = 3000
13. Rc = 2000
Rd = 1000
Vs = 12 v
We need to figure out where we can start. We can start by trying
to find any of the combinations we've learned about. So let's think about
whether there are any series or parallel combinations and if there are
let's see if we can identify them. Then we can apply what we know about
series and parallel combinations. There's no guarantee that approach will
work, but it is worth a try. Let's look at two resistors at a time.
The first question is are there any series or parallel combinations?
Click the red button below to see two resistors in series.
Question
Q6 Would the two resistors above (highlighted when the button is
clicked) be in series if any current were drawn from the circuit by
attaching a load?
Now, we should be able to replace the two resistors in series with
their series equivalent. If we do that, there's a node in the middle with a
voltage, and we'll lose information about that voltage. Right now, we're
14. not interested in that voltage, and we'll willing to lose that information.
Let's just replace the two resistors with their series equivalent. Click
the red button to make that replacement. Depressing the button will
remove the two resistors in series, and releasing the button will insert
the replacement.
Now you should have the circuit with the two resistors in series
replaced by their series equivalent. Now, we can see that there is
another replacement we can make. What's that replacement?
Question
Q7 What replacement can be made?
Ok, you see how it goes. Let's take a numerical example using the
values mentioned above.
Ra = 1500
Rb = 3000
Rc = 2000
Rd = 1000
Vs = 12 v
Here is the circuit.
15. Problems
P12. What is the equivalent resistance of the two resistors in series -
1000 and 2000 ?
Your grade is:
P13. Next you should have two resistors in parallel. What is the parallel
equivalent?
Your grade is:
P14. Now you should have two resistors in series attached to the source.
What is the value of the series equivalent?
Your grade is:
P15. With a 12v source - as shown in the figure - what is the current
that is drawn from the source? Give your answer in amperes here.
16. Your grade is:
Give your answer in milliamperes here, if that's what you want.
Your grade is:
Problems
Problem Resist2P01 - Resistor Combinations - 1
Problem Resist2P02 - Resistor Combinations - 2
Problem Resist2P03 - Resistor Combinations - 3
Problem Resist2P04 - Resistor Combinations - 4
Problem Resist2P05 - Resistor Combinations - 5
Links to Other Lessons on Resistors
Resistors
RCombinations
VoltageDividers
Bridge Circuits
Resistance Experiments
Send your comments on these lessons.