This document outlines the key learning objectives and content covered in Chapter 20 on Electric Circuits. The chapter covers current, resistance, power, Ohm's law, series and parallel circuits, capacitors, and more. The learning objectives are to understand concepts like current, conductivity, resistance, Ohm's law, and how resistors behave in series and parallel combinations. Students should be able to apply concepts like equivalent resistance, voltage division, and Kirchhoff's rules to solve circuit problems. The chapter also covers capacitors and RC circuits.
Resistors are used in electric circuits to oppose electric current and are measured in ohms. They have two main characteristics - resistance value and power dissipation capacity. Resistors come in various resistance values and tolerances, and are used for purposes like heating and current limiting. They can be fixed or variable, and fixed resistors include carbon composition, metalized, and wire wound types. Variable resistors have three leads - two fixed and one movable - to allow adjustment of resistance while connected to a circuit.
This document discusses star and delta connections in 3-phase power systems. It provides symbols and diagrams to illustrate star and delta configurations. Key differences are noted, such as star connections providing a neutral point and being used for lower voltages, while delta connections having no neutral and being used for higher voltages. Formulas are presented relating line and phase voltages and currents for each connection type. Examples are worked through applying the formulas to calculate line voltage from phase voltage in a star-connected motor, and to calculate line current from phase current in a delta-connected motor.
Electric current is the flow of electric charge. It is measured in amperes (A) which is equal to one coulomb of charge passing through an area in one second. Ohm's law states that the current through a conductor is directly proportional to the voltage applied across it. Resistance is a measure of how an object impedes the flow of current and is equal to the voltage divided by the current. Power is equal to the current times the voltage and describes the rate at which electrical energy is transferred by a circuit.
The document introduces basic concepts of electric circuits including charge, current, voltage, power, and circuit elements. It defines each concept, provides examples, and shows calculations for determining values like charge from given quantities of electrons or protons. Key points covered include that charge is measured in Coulombs, current in Amperes, voltage in volts, and power in watts. Circuit elements can be active sources or passive components that absorb energy.
- Alternating current changes direction periodically in a sine wave pattern. The frequency is measured in Hertz (Hz), typically 50 or 60 Hz.
- AC can transmit power over longer distances with less power loss than direct current. AC voltages can be increased or decreased using transformers.
- Important AC terms include root mean square (RMS) value, phase angle, impedance, and resonance. Resonance occurs when the capacitive and inductive reactances cancel out, resulting in maximum current. Circuits can resonate in series or parallel configurations.
This document provides an overview of basic electronics concepts including lattices, semiconductors, diodes, and transistors. It begins by defining lattices and their applications in mathematics. It then discusses superconductors, insulators, intrinsic and extrinsic semiconductors, and the band theory of conduction. Diodes and rectifiers are introduced, including half-wave and full-wave rectification circuits. The document concludes by explaining transistors, including bipolar junction transistors with npn and pnp configurations and their characteristics curves. Transistors are shown to have applications as amplifiers and switches in devices like LED spotlights and single transistor radios.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Inductors store energy in the form of a magnetic field and deliver it when needed. An inductor consists of a coil of wire wrapped around a ferromagnetic core. The three main factors that affect inductance are the number of turns in the coil, the permeability of the core material, and the size of the core. There are three main types of fixed inductors: air core inductors which have the lowest inductance, iron core inductors which are useful at low frequencies, and ferrite core inductors which are used for high frequency applications due to their high resistivity and lack of hysteresis losses.
Resistors are used in electric circuits to oppose electric current and are measured in ohms. They have two main characteristics - resistance value and power dissipation capacity. Resistors come in various resistance values and tolerances, and are used for purposes like heating and current limiting. They can be fixed or variable, and fixed resistors include carbon composition, metalized, and wire wound types. Variable resistors have three leads - two fixed and one movable - to allow adjustment of resistance while connected to a circuit.
This document discusses star and delta connections in 3-phase power systems. It provides symbols and diagrams to illustrate star and delta configurations. Key differences are noted, such as star connections providing a neutral point and being used for lower voltages, while delta connections having no neutral and being used for higher voltages. Formulas are presented relating line and phase voltages and currents for each connection type. Examples are worked through applying the formulas to calculate line voltage from phase voltage in a star-connected motor, and to calculate line current from phase current in a delta-connected motor.
Electric current is the flow of electric charge. It is measured in amperes (A) which is equal to one coulomb of charge passing through an area in one second. Ohm's law states that the current through a conductor is directly proportional to the voltage applied across it. Resistance is a measure of how an object impedes the flow of current and is equal to the voltage divided by the current. Power is equal to the current times the voltage and describes the rate at which electrical energy is transferred by a circuit.
The document introduces basic concepts of electric circuits including charge, current, voltage, power, and circuit elements. It defines each concept, provides examples, and shows calculations for determining values like charge from given quantities of electrons or protons. Key points covered include that charge is measured in Coulombs, current in Amperes, voltage in volts, and power in watts. Circuit elements can be active sources or passive components that absorb energy.
- Alternating current changes direction periodically in a sine wave pattern. The frequency is measured in Hertz (Hz), typically 50 or 60 Hz.
- AC can transmit power over longer distances with less power loss than direct current. AC voltages can be increased or decreased using transformers.
- Important AC terms include root mean square (RMS) value, phase angle, impedance, and resonance. Resonance occurs when the capacitive and inductive reactances cancel out, resulting in maximum current. Circuits can resonate in series or parallel configurations.
This document provides an overview of basic electronics concepts including lattices, semiconductors, diodes, and transistors. It begins by defining lattices and their applications in mathematics. It then discusses superconductors, insulators, intrinsic and extrinsic semiconductors, and the band theory of conduction. Diodes and rectifiers are introduced, including half-wave and full-wave rectification circuits. The document concludes by explaining transistors, including bipolar junction transistors with npn and pnp configurations and their characteristics curves. Transistors are shown to have applications as amplifiers and switches in devices like LED spotlights and single transistor radios.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Inductors store energy in the form of a magnetic field and deliver it when needed. An inductor consists of a coil of wire wrapped around a ferromagnetic core. The three main factors that affect inductance are the number of turns in the coil, the permeability of the core material, and the size of the core. There are three main types of fixed inductors: air core inductors which have the lowest inductance, iron core inductors which are useful at low frequencies, and ferrite core inductors which are used for high frequency applications due to their high resistivity and lack of hysteresis losses.
Semiconductor Diode :
What is Semiconductor Diode?
How is it Work?
What are the Types?
Current Flow in Forward And Reverse Bios?
What is Light Emitting Diode (LED)?
What is Zener Diode?
and in aditional :
P-N Junction and its formation
Formation of Depletion Layer
External Biasing of P-N Junction
V-I Characteristics of P-N Junction
Zener Breakdown
Avalanche Breakdown
Comparison between Zener and Avalanche Breakdown
- Tesla proposed using transformers in power distribution systems to step up voltage for transmission and step down voltage for consumption, reducing power losses.
- A transformer consists of coils wrapped around a common core and converts AC voltage from one level to another at the same frequency through electromagnetic induction.
- Transformers allow impedance matching between generation/transmission systems and distribution/consumption systems through voltage transformation ratios.
This document provides an overview of key concepts in electric circuits including:
1. An electric circuit connects an energy source to an energy consuming device through conducting wires that allow electric charges to move. Electromotive force drives current, measured in amperes, through a circuit.
2. Ohm's law defines the relationship between voltage, current, and resistance. Resistance depends on the material's resistivity and dimensions. Components like resistors control current in circuits.
3. Electric power, measured in watts, is calculated by multiplying voltage by current. This relates to the energy delivered by a circuit over time for devices that function as resistors.
This document provides information on resistors, including different types of resistors, resistor color coding, and evaluating resistors based on their color bands. It discusses:
- The main types of resistors are fixed value resistors, variable resistors, and package resistors. Resistors can also be classified based on their composition, such as carbon deposition, carbon composition, metal film, and wire wound resistors.
- Resistor color coding uses color bands to identify the nominal resistance value and tolerance. Four-band resistors indicate values with ±5% and ±10% tolerance, while five-band resistors have ±1% and ±2% tolerance.
- Examples are provided of interpreting resistance values from the color bands on four-
This document provides an outline and overview of key concepts in alternating current (AC) circuits including:
1. AC sources and how AC voltage and current vary sinusoidally over time.
2. The behavior of resistors, inductors, and capacitors in AC circuits, including how their current and voltage are phase shifted.
3. Series RLC circuits and the concept of resonance where the current is at its maximum.
4. Power calculations in AC circuits and the power factor.
5. Transformers and how they are used for power transmission. Electrical filters are also discussed.
A resistor is an electrical component that opposes or resists the flow of electric current. It works by converting electrical energy into heat energy as current passes through it. Resistors are commonly used to regulate current and voltage levels in electronic circuits. They come in various types defined by their material and manufacturing process, and their resistance values are color coded for easy identification.
1. The Kelvin bridge is a modified Wheatstone bridge used to accurately measure low resistances. It accounts for contact resistance by using four-terminal connections.
2. In a Kelvin bridge, the unknown resistance is connected between two potential terminals to directly measure its value, independent of contact resistance at the current terminals.
3. The bridge balances when the galvanometer is connected to a point between the potential terminals that divides the lead resistance into two equal parts, nullifying its effect on the measurement.
This document discusses semiconductor diodes and rectifiers. It begins by explaining the physical principles of semiconductors, including intrinsic semiconductors and how doping with materials like phosphorus or boron creates n-type and p-type semiconductors. When a p-type and n-type material meet, it forms a pn junction with interesting electrical properties. Diodes are made from pn junctions and exhibit asymmetric conduction, allowing current in one direction but blocking it in the other. Diode circuits and models are also covered, along with important applications like rectification where diodes are used to convert AC to DC power.
This document summarizes key concepts in electrostatics including:
1) Electrostatics is the study of properties of electric charges at rest. Charges of the same type repel and opposite charges attract based on Coulomb's law.
2) Coulomb's law states that the electrical force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
3) Electric field is defined as the force experienced by a unit positive charge placed at a point in an electric field. Electric field lines represent the direction of the electric field.
The document discusses electric potential difference, electric circuits, electrical resistance, and electrical power and energy. It explains that electric potential difference is the work required to move a charge between two points, defines electric circuits and current, describes resistance as a measure of how much a material hinders the flow of electric current, and introduces the concepts of electrical power and energy relating voltage, current, resistance, and time in circuits.
The document discusses alternating current (AC) and provides details about its key characteristics:
1) AC electricity alternates direction periodically in a back-and-forth motion, unlike direct current which flows in one direction.
2) The instantaneous value of AC varies sinusoidally over time between a maximum and minimum value.
3) Common applications of AC include power transmission and use in homes/businesses due to advantages like easy voltage transformation.
ELECTROSTATICS OF CONDUCTORS AND DIELECTRICSSheeba vinilan
The document discusses the properties of conductors at electrostatic equilibrium. It states that conductors contain mobile charges that are free to move, like electrons in metals. When no electric field is present, these charges are randomly distributed. At equilibrium, there is no net electric field inside the conductor. The electric field outside is perpendicular to the surface and its magnitude depends on the surface charge density. The potential is constant across the surface and interior.
The document discusses the basic components and relationships in electrical circuits. It explains that all circuits require a voltage source to provide energy to electrons, a conductor to carry the electrons, and a load or resistance where energy is extracted. It defines key electrical quantities like voltage, current, resistance, and Ohm's Law, which states that current is directly proportional to voltage and inversely proportional to resistance. The document also discusses how internal resistance affects the terminal voltage available from a source.
An electric circuit is a path in which electrons from a voltage or current source flow. The point where those electrons enter an electrical circuit is called the "source" of electrons.
1. The document discusses electric cells and their components including electromotive force (EMF), terminal potential difference, and internal resistance.
2. It explains that an electric cell converts chemical energy into electrical energy through a chemical reaction between two electrodes immersed in an electrolyte.
3. The document provides details on different types of cells such as primary cells that cannot be recharged and secondary cells that can be recharged, and discusses factors that affect a cell's internal resistance.
This document discusses key concepts in electric circuits including potential difference, electromotive force (emf), current, resistance, and how these concepts relate to different circuit configurations. It defines potential difference and emf as the voltage across battery terminals when not or in a complete circuit. Current is defined as the rate of charge flow measured in amperes. Resistance depends on the material and physical characteristics of a circuit element and is measured in ohms. Resistors in series have the same current but their voltages add up, while resistors in parallel have the same voltage but their currents add up. Measuring devices like voltmeters and ammeters must be connected appropriately.
The document discusses different aspects of electric charge including:
1) Atoms contain protons, neutrons, and electrons. Objects with equal numbers of protons and electrons are neutral, while imbalances lead to electric charges.
2) Charged objects exert electric forces on each other - opposites attract and likes repel. The elementary charge unit is 1 electron or proton.
3) Neutral objects can become polarized when near a charged object, gaining opposite charges on opposite sides and becoming attracted to both positive and negative charges.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
This document provides an overview of key concepts in rotational kinematics covered in Chapter 8, including angular displacement, velocity, and acceleration. It defines these rotational variables and their relationships to linear motion. Examples are given to illustrate calculating angular variables and transforming between rotational and tangential linear motion for objects like rolling wheels or helicopter blades. Formulas for rotational kinematics with constant angular acceleration are also presented.
This document provides an overview of key physics concepts and mathematical tools. It covers units of measurement in the SI system, vector notation and operations like addition/subtraction, trigonometry, and dimensional analysis. Example problems demonstrate various concepts like finding components of vectors and adding multiple vectors. The document concludes with additional mathematical rules and functions important for physics problems.
Semiconductor Diode :
What is Semiconductor Diode?
How is it Work?
What are the Types?
Current Flow in Forward And Reverse Bios?
What is Light Emitting Diode (LED)?
What is Zener Diode?
and in aditional :
P-N Junction and its formation
Formation of Depletion Layer
External Biasing of P-N Junction
V-I Characteristics of P-N Junction
Zener Breakdown
Avalanche Breakdown
Comparison between Zener and Avalanche Breakdown
- Tesla proposed using transformers in power distribution systems to step up voltage for transmission and step down voltage for consumption, reducing power losses.
- A transformer consists of coils wrapped around a common core and converts AC voltage from one level to another at the same frequency through electromagnetic induction.
- Transformers allow impedance matching between generation/transmission systems and distribution/consumption systems through voltage transformation ratios.
This document provides an overview of key concepts in electric circuits including:
1. An electric circuit connects an energy source to an energy consuming device through conducting wires that allow electric charges to move. Electromotive force drives current, measured in amperes, through a circuit.
2. Ohm's law defines the relationship between voltage, current, and resistance. Resistance depends on the material's resistivity and dimensions. Components like resistors control current in circuits.
3. Electric power, measured in watts, is calculated by multiplying voltage by current. This relates to the energy delivered by a circuit over time for devices that function as resistors.
This document provides information on resistors, including different types of resistors, resistor color coding, and evaluating resistors based on their color bands. It discusses:
- The main types of resistors are fixed value resistors, variable resistors, and package resistors. Resistors can also be classified based on their composition, such as carbon deposition, carbon composition, metal film, and wire wound resistors.
- Resistor color coding uses color bands to identify the nominal resistance value and tolerance. Four-band resistors indicate values with ±5% and ±10% tolerance, while five-band resistors have ±1% and ±2% tolerance.
- Examples are provided of interpreting resistance values from the color bands on four-
This document provides an outline and overview of key concepts in alternating current (AC) circuits including:
1. AC sources and how AC voltage and current vary sinusoidally over time.
2. The behavior of resistors, inductors, and capacitors in AC circuits, including how their current and voltage are phase shifted.
3. Series RLC circuits and the concept of resonance where the current is at its maximum.
4. Power calculations in AC circuits and the power factor.
5. Transformers and how they are used for power transmission. Electrical filters are also discussed.
A resistor is an electrical component that opposes or resists the flow of electric current. It works by converting electrical energy into heat energy as current passes through it. Resistors are commonly used to regulate current and voltage levels in electronic circuits. They come in various types defined by their material and manufacturing process, and their resistance values are color coded for easy identification.
1. The Kelvin bridge is a modified Wheatstone bridge used to accurately measure low resistances. It accounts for contact resistance by using four-terminal connections.
2. In a Kelvin bridge, the unknown resistance is connected between two potential terminals to directly measure its value, independent of contact resistance at the current terminals.
3. The bridge balances when the galvanometer is connected to a point between the potential terminals that divides the lead resistance into two equal parts, nullifying its effect on the measurement.
This document discusses semiconductor diodes and rectifiers. It begins by explaining the physical principles of semiconductors, including intrinsic semiconductors and how doping with materials like phosphorus or boron creates n-type and p-type semiconductors. When a p-type and n-type material meet, it forms a pn junction with interesting electrical properties. Diodes are made from pn junctions and exhibit asymmetric conduction, allowing current in one direction but blocking it in the other. Diode circuits and models are also covered, along with important applications like rectification where diodes are used to convert AC to DC power.
This document summarizes key concepts in electrostatics including:
1) Electrostatics is the study of properties of electric charges at rest. Charges of the same type repel and opposite charges attract based on Coulomb's law.
2) Coulomb's law states that the electrical force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
3) Electric field is defined as the force experienced by a unit positive charge placed at a point in an electric field. Electric field lines represent the direction of the electric field.
The document discusses electric potential difference, electric circuits, electrical resistance, and electrical power and energy. It explains that electric potential difference is the work required to move a charge between two points, defines electric circuits and current, describes resistance as a measure of how much a material hinders the flow of electric current, and introduces the concepts of electrical power and energy relating voltage, current, resistance, and time in circuits.
The document discusses alternating current (AC) and provides details about its key characteristics:
1) AC electricity alternates direction periodically in a back-and-forth motion, unlike direct current which flows in one direction.
2) The instantaneous value of AC varies sinusoidally over time between a maximum and minimum value.
3) Common applications of AC include power transmission and use in homes/businesses due to advantages like easy voltage transformation.
ELECTROSTATICS OF CONDUCTORS AND DIELECTRICSSheeba vinilan
The document discusses the properties of conductors at electrostatic equilibrium. It states that conductors contain mobile charges that are free to move, like electrons in metals. When no electric field is present, these charges are randomly distributed. At equilibrium, there is no net electric field inside the conductor. The electric field outside is perpendicular to the surface and its magnitude depends on the surface charge density. The potential is constant across the surface and interior.
The document discusses the basic components and relationships in electrical circuits. It explains that all circuits require a voltage source to provide energy to electrons, a conductor to carry the electrons, and a load or resistance where energy is extracted. It defines key electrical quantities like voltage, current, resistance, and Ohm's Law, which states that current is directly proportional to voltage and inversely proportional to resistance. The document also discusses how internal resistance affects the terminal voltage available from a source.
An electric circuit is a path in which electrons from a voltage or current source flow. The point where those electrons enter an electrical circuit is called the "source" of electrons.
1. The document discusses electric cells and their components including electromotive force (EMF), terminal potential difference, and internal resistance.
2. It explains that an electric cell converts chemical energy into electrical energy through a chemical reaction between two electrodes immersed in an electrolyte.
3. The document provides details on different types of cells such as primary cells that cannot be recharged and secondary cells that can be recharged, and discusses factors that affect a cell's internal resistance.
This document discusses key concepts in electric circuits including potential difference, electromotive force (emf), current, resistance, and how these concepts relate to different circuit configurations. It defines potential difference and emf as the voltage across battery terminals when not or in a complete circuit. Current is defined as the rate of charge flow measured in amperes. Resistance depends on the material and physical characteristics of a circuit element and is measured in ohms. Resistors in series have the same current but their voltages add up, while resistors in parallel have the same voltage but their currents add up. Measuring devices like voltmeters and ammeters must be connected appropriately.
The document discusses different aspects of electric charge including:
1) Atoms contain protons, neutrons, and electrons. Objects with equal numbers of protons and electrons are neutral, while imbalances lead to electric charges.
2) Charged objects exert electric forces on each other - opposites attract and likes repel. The elementary charge unit is 1 electron or proton.
3) Neutral objects can become polarized when near a charged object, gaining opposite charges on opposite sides and becoming attracted to both positive and negative charges.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
This document provides an overview of key concepts in rotational kinematics covered in Chapter 8, including angular displacement, velocity, and acceleration. It defines these rotational variables and their relationships to linear motion. Examples are given to illustrate calculating angular variables and transforming between rotational and tangential linear motion for objects like rolling wheels or helicopter blades. Formulas for rotational kinematics with constant angular acceleration are also presented.
This document provides an overview of key physics concepts and mathematical tools. It covers units of measurement in the SI system, vector notation and operations like addition/subtraction, trigonometry, and dimensional analysis. Example problems demonstrate various concepts like finding components of vectors and adding multiple vectors. The document concludes with additional mathematical rules and functions important for physics problems.
Ch 27 interference & wave nature of light onlineScott Thomas
The document discusses key concepts related to the wave nature of light and interference and diffraction phenomena:
1) Interference occurs when two light waves pass through a point and their electric fields combine according to the principle of superposition, resulting in constructive or destructive interference depending on whether the waves are in or out of phase.
2) Young's double-slit experiment demonstrates interference, producing bright and dark fringes on a screen from the constructive and destructive interference of light passing through two slits.
3) Thin-film interference results from the multiple reflections within a thin film, leading to either constructive or destructive interference depending on the path length differences and refractive indices of the materials.
This document provides an overview of Newtonian mechanics and one-dimensional kinematics. It defines key terms like position, velocity, acceleration, displacement, distance, speed, average speed, average velocity, instantaneous velocity, constant acceleration, and the kinematic equations. It includes examples of how to use the kinematic equations to solve problems involving constant acceleration. There are also sample problems assessing understanding of concepts like displacement vs distance, velocity, acceleration, and interpreting graphs of kinematic variables.
This document discusses uniform circular motion and related concepts like centripetal acceleration and centripetal force. It covers topics like how radius, speed and acceleration are related in uniform circular motion; the direction of velocity and acceleration vectors; forces that cause an object to travel in a circular path like friction or the normal force on a banked curve; and applications involving objects moving in horizontal and vertical circles like cars on curved roads. The document contains learning objectives, definitions, examples, questions and sections on key ideas like centripetal acceleration, centripetal force and banked curves.
The document provides learning objectives and content for a chapter on thermodynamics. It covers key concepts like the first and second laws of thermodynamics, thermal processes, and using the ideal gas law. For thermal processes using ideal gases, it defines equations for isothermal, adiabatic, isobaric and isochoric processes. Examples are provided for calculating work done during isothermal expansion of an ideal gas and adiabatic compression. The chapter sections will address thermodynamic systems, the laws of thermodynamics, thermal processes, processes for ideal gases, and applications like heat engines and entropy.
This document provides learning objectives and content outlines for an AP Physics chapter on electric forces and electric fields. It begins by listing key concepts students should understand related to electrostatics, including charge, Coulomb's law, and the electric field. It then provides an outline of the chapter sections, which cover the origin of electricity, charged objects and the electric force, conductors and insulators, methods of charging, Coulomb's law, the electric field, and other topics. Tables of contents and examples are also included.
Ch19 Electric Potential Energy and Electric PotentialScott Thomas
This document provides learning objectives and content about electric potential energy and electric potential. It discusses key concepts such as electric field, electric potential, equipotential surfaces, and capacitors. Specifically, it defines electric potential as electric potential energy per unit charge. It also explains that equipotential surfaces represent positions of equal electric potential and that the electric field is perpendicular to equipotential surfaces. Finally, it introduces capacitors as devices that can store electric potential energy between two conductors, such as the plates of a parallel plate capacitor, and how dielectrics are used to increase a capacitor's capacitance.
A document discusses conductors, capacitors, dielectrics, electric fields and forces, important concepts in electricity including circuits, capacitors, and formulas. Key points include:
- Conductors allow free movement of electrons while dielectrics are electrical insulators.
- Electric fields exist around charged objects and point in the direction of force on a positive test charge. Capacitance depends on physical characteristics like plate area and separation.
- Circuits can be series or parallel. Kirchhoff's rules are used to solve complex circuit problems regarding potential and current.
- Capacitors store electric charge between conductors separated by a dielectric. They function to block DC and pass AC current.
The document summarizes key concepts about electric circuits, including:
- An electric circuit connects an energy source to a device using conducting wires for electric charge to flow. Current is the rate of charge flow.
- Ohm's law defines the relationship between voltage, current, and resistance in a circuit. Resistance depends on the material's resistivity, length, and cross-sectional area.
- Power in a circuit is defined as the product of voltage and current. It describes the rate at which energy is transferred by the electric current.
- Circuits can have components connected in series, parallel, or a combination. Kirchhoff's laws describe the analysis of current and voltage in such circuits.
This document discusses electric circuits and Ohm's law. It provides examples of calculating current, resistance, voltage, and power in both series and parallel circuits. Key points covered include:
- Ohm's law defines the relationship between voltage, current, and resistance in a circuit.
- Components in series experience the same current but their voltages add up. The total resistance is the sum of the individual resistances.
- Components in parallel experience the same voltage but their currents combine. The total resistance is lower than any individual resistance.
- Power is calculated as the product of voltage and current, and describes how much energy is used by components in a circuit.
The document summarizes key concepts about electrical quantities including current, resistance, voltage, power and energy. It defines current as the flow of electric charge and explains that current is measured using an ammeter. Resistance is defined as the ratio of voltage to current and depends on the length and cross-sectional area of a conductor. Voltage or potential difference is the work required to move a unit charge between two points and is measured using a voltmeter. Power is the rate at which electrical energy is transferred and is calculated by multiplying current and voltage. Energy is calculated by multiplying power by time.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts like EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Describing resistance at a microscopic level and defining related concepts like resistivity and conductance.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts such as EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Describing resistance at a microscopic level and defining related concepts like resistivity and conductance.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts like EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Describing resistance at a microscopic level and defining related concepts like resistivity and conductance.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts like EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Describing resistance at a microscopic level and defining related concepts like resistivity and conductance.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts like EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Giving a microscopic description of resistance in wires using concepts like resistivity and conductivity.
4) Covering related practical work using equipment like voltmeters and capacitors.
MOST IMPORTANT QUESTIONS FOR CURRENT ELECTRICITY CBSE XII BY ATCDeepankur Rastogi
This document contains a 30 question physics exam on topics related to current and electricity for Class XII. The exam covers concepts such as superconductors, current, resistance, Ohm's law, circuits, and applications of electricity. Questions involve calculations related to resistors, current, power, and electric cells. Diagrams and derivations of formulas are also assessed. The exam is designed based on the new CBSE board examination pattern for 2013-14.
This document discusses electric current and direct current circuits. It begins by providing an analogy comparing voltage, resistance, and current to gravity, friction, and the flow of water in a river. It then defines electric current microscopically as the drift velocity of electrons in a metal when an electric field is applied. It provides the formula for current as the rate of flow of charge. Several examples are worked through applying this formula. The document continues by defining Ohm's law and resistivity. It explains how resistance depends on the properties and dimensions of the conductor. Finally, it discusses how resistance varies with temperature and defines the temperature coefficient of resistivity.
Electric current is the flow of electric charge through a conductor. It is measured in amperes. Current is directly proportional to the rate of flow of charge and inversely proportional to the time taken. Resistance is a measure of how difficult it is for current to flow through a material. It depends on the material's resistivity as well as the conductor's length and cross-sectional area. Ohm's Law states that current is directly proportional to voltage for conductors that obey Ohm's Law. Resistance increases with length or decreases with cross-sectional area for a given material according to the formula for resistivity.
This document provides an overview of key concepts in electric circuits including:
1) An electric circuit connects an energy source to an energy consuming device through conducting wires that allow electric charges to move. Within a battery, a chemical reaction transfers electrons from one terminal to another, creating an electromotive force (emf).
2) Ohm's law defines resistance as the ratio between voltage and current. Resistance opposes electric current in a circuit. Resistors are used to control current in circuits like light bulbs.
3) Circuits can be wired in series, where the same current flows through all components, or parallel, where the same voltage is applied across all components allowing more current to be drawn than
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2. Learning Objectives
Electric circuits
Current, resistance, power
Students should understand the definition of electric
current, so they can relate the magnitude and direction of
the current to the rate of flow of positive and negative
charge.
Students should understand conductivity, resistivity, and
resistance, so they can:
Relate current and voltage for a resistor.
Describe how the resistance of a resistor depends upon
its length and cross-sectional area, and apply this result
in comparing current flow in resistors of different
material or different geometry.
Apply the relationships for the rate of heat production in
a resistor.
3. Learning Objectives
Steady-state direct current circuits with batteries and
resistors only
Students should understand the behavior of series and
parallel combinations of resistors, so they can:
Identify on a circuit diagram whether resistors are in
series or in parallel.
Determine the ratio of the voltages across resistors
connected in series or the ratio of the currents through
resistors connected in parallel.
Calculate the equivalent resistance of a network of
resistors that can be broken down into series and
parallel combinations.
Calculate the voltage, current, and power dissipation for
any resistor in such a network of resistors connected to
a single power supply.
Design a simple series-parallel circuit that produces a
given current through and potential difference across
one specified component, and draw a diagram for the
circuit using conventional symbols.
4. Learning Objectives
Steady-state direct current circuits with batteries and
resistors only
Students should understand the properties of ideal and real
batteries, so they can:
Calculate the terminal voltage of a battery of specified
emf and internal resistance from which a known current
is flowing.
Students should be able to apply Ohm’s law and
Kirchhoff’s rules to direct-current circuits, in order to:
determine a single unknown current, voltage, or resistance.
Students should understand the properties of voltmeters
and ammeters, so they can:
State whether the resistance of each is high or low.
Identify or show correct methods of connecting meters
into circuits in order to measure voltage or current.
5. Learning Objectives
Capacitors in circuits
Students should understand the t = 0 and steady-state
behavior of capacitors connected in series or in parallel, so
they can:
Calculate the equivalent capacitance of a series or
parallel combination.
Describe how stored charge is divided between
capacitors connected in parallel.
Determine the ratio of voltages for capacitors connected
in series.
Calculate the voltage or stored charge, under steady-
state conditions, for a capacitor connected to a circuit
consisting of a battery and resistors.
6. Table of Contents
1. Electromotive Force and Current
2. Ohm’s Law
3. Resistance & Resistivity
4. Electric Power
5. Alternating Current (Not AP)
6. Series Wiring
7. Parallel Wiring
8. Series and Parallel Wiring
9. Internal Resistance
10. Kirchoff’s Rules
11. The Measurement of Current and Voltage
12. Capacitors in Series and Parallel Circuits
13. RC Circuits (Not AP)
14. Safety and the Physiological Effects of Current (Not AP)
8. Electric Circuits
In an electric circuit, an energy source and an energy
consuming device are connected by conducting wires through
which electric charges move.
9. Electromotive Force
Within a battery, a chemical reaction occurs that transfers
electrons from one terminal to another terminal.
The maximum potential difference across the terminals is
called the electromotive force (emf).
10. The electric current is the amount of charge per unit time
that passes through a surface that is perpendicular to the
motion of the charges.
t
Q
Iavg
∆
∆
=
One coulomb per second equals one ampere (A).
Electric Current
11. Types of Current
If the charges move around the circuit in the same direction at
all times, the current is said to be direct current (dc).
If the charges move first one way and then the opposite way,
the current is said to be alternating current (ac).
12. Example 1 A Pocket Calculator
The current in a 3.0 V battery of a pocket calculator is 0.17 mA. In one hour
of operation, (a) how much charge flows in the circuit and (b) how much energy
does the battery deliver to the calculator circuit?
(a)
(b)
( )tIQ ∆=∆
( )( )V0.3C61.0=
t
Q
Iavg
∆
∆
=
( )( )s3600A1017.0 3−
×= C61.0=
QVU = J8.1=
13. Direction of Current
Conventional current is the hypothetical flow of positive
charges that would have the same effect in the circuit as the
movement of negative charges that actually does occur.
14. 20.1.1. In which one of the following situations does a conventional
electric current flow due north?
a) Protons in a beam are moving due south.
b) A water molecule is moving due north.
c) Electrons in a beam are moving due south.
d) Electrons in a wire connected to a battery are moving from south
to north.
15. 20.1.2. The battery capacity of a lithium ion battery in a digital
music player is 750 mA-h. The manufacturer claims that the player
can operate for eight hours if the battery is initially fully charged.
Given this information, determine the number of electrons that flow
through the player as you listen to your favorite songs for three hours.
a) 6.2 × 1018
electrons
b) 1.0 × 103
electrons
c) 2.4 × 109
electrons
d) 6.3 × 1021
electrons
e) 8.1 × 1028
electrons
17. Resistance
The resistance (R) is defined as
the ratio of the voltage V applied
across a piece of material to the
current I through the material.
To the extent that a wire or an
electrical device offers resistance
to electrical flow, it is called a
resistor.
18. SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω)
I∝V
Ohm’s Law
The V is proportional to I,
where V is the voltage applied
across a piece of material and
I is the current through the
material:
IRV =
19. Example 2 A Flashlight
The filament in a light bulb is a resistor in the form
of a thin piece of wire. The wire becomes hot enough
to emit light because of the current in it. The flashlight
uses two 1.5-V batteries to provide a current of
0.40 A in the filament. Determine the resistance of
the glowing filament.
I
V
R =
IRV =
A0.40
V0.3
= Ω= 5.7
20. 20.2.1. In a certain circuit containing a battery and a resistor, Ohm’s law is obeyed.
An instrument to measure the current in the circuit, an ammeter, is connected in
between one of the terminals of the battery and one end of the resistor. The ammeter
indicates that the current in the circuit is I. The battery is then removed and replaced
with another battery. This time, the ammeter indicates the current is 2I. Which one of
the following statements concerning the resistor is true?
a) When the second battery was placed in the circuit, the resistance increased to twice its
initial value.
b) When the second battery was placed in the circuit, the resistance decreased to one half its
initial value.
c) When the second battery was placed in the circuit, the resistance increased to four times
its initial value.
d) When the second battery was placed in the circuit, the resistance increased to one fourth
its initial value.
e) When the second battery was placed in the circuit, the resistance did not change.
21. 20.2.2. Consider the circuit containing a battery and a resistor shown.
For which one of the following combinations of current and
voltage does R have the smallest value?
a) V = 9 V and I = 0.002 A
b) V = 12 V and I = 0.5 A
c) V = 1.5 V and I = 0.075 A
d) V = 6 V and I = 0.1 A
e) V = 4.5 V and I = 0.009 A
22. 20.2.3. A certain circuit contains a battery and a resistor. An instrument to measure the current in
the circuit, an ammeter, is connected in between one of the terminals of the battery and one
end of the resistor. The graph shows the current in the circuit as the voltage is increased.
Which one of the following statements best describes the resistor in this circuit?
a) The resistor does not
obey Ohm’s law.
b) The resistor obeys Ohm’s
law for voltages between zero
and twenty-five volts.
c) The resistor obeys Ohm’s law
for voltages between zero and
thirty-five volts.
d) The resistor obeys Ohm’s law for
voltages between zero and forty volts.
e) The resistor obeys Ohm’s law for voltages between thirty and forty volts.
24. A
L
R
ρ
=
resistivity in units of ohm·meter
Resistance in Materials
For a wide range of materials, the resistance of a piece of
material of length L and cross-sectional area A is:
25.
26. Example 3 Longer Extension Cords
The instructions for an electric lawn mower suggest that a 20-gauge extension
cord can be used for distances up to 35 m, but a thicker 16-gauge cord should
be used for longer distances. The cross sectional area of a
20-gauge wire is 5.2x10-7
Ω·m, while that of a 16-gauge wire is 13x10-7
Ω·m.
Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of
16-gauge copper wire.
A
L
R
ρ
=
(a)
(b) ( )( )
27-
8
m1013
m75m1072.1
×
⋅Ω×
=
−
( )( )
27-
8
m105.2
m35m1072.1
×
⋅Ω×
=
−
Ω= 2.1
A
L
R
ρ
= Ω= 99.0
27. ( )[ ]oo TT −+= αρρ 1
temperature coefficient
of resistivity
( )[ ]oo TTRR −+= α1
Temperature Effects
28. 20.3.1. For which combination for the length L and radius R of a wire
will the resistance have the smallest value?
a) L = 0.50 m and R = 0.03 m
b) L = 0.25 m and R = 0.08 m
c) L = 0.40 m and R = 0.2 m
d) L = 0.80 m and R = 0.1 m
e) L = 0.10 m and R = 0.05 m
29. 20.3.2. The ends of a wire are connected to the terminals of a battery.
For which of the following changes will the resulting current in the
circuit have the largest value?
a) Replace the wire with one that has a larger resistivity.
b) Replace the wire with one that has a larger radius.
c) Replace the wire with one that has a longer length.
32. IVP =
SI Unit of Power: watt (W)
( ) RIIRIP 2
==
R
V
V
R
V
P
2
=
=
Electric Power
When there is current in a circuit as a result of a voltage, the
electric power delivered to the circuit is:
33. Example 5 The Power and Energy Used in a
Flashlight
In the flashlight, the current is 0.40A and the voltage
is 3.0 V. Find (a) the power delivered to the bulb and
(b) the energy dissipated in the bulb in 5.5 minutes
of operation.
(a)
(b)
IVP =
PtE =
( )( )V0.3A40.0= W2.1=
( )( )s330W2.1= J100.4 2
×=
34. 20.4.1. An automatic coffee maker uses a resistive heating element to boil
the 2.4 kg of water that was poured into it at 21 °C. The current
delivered to the coffee pot is 8.5 A when it is plugged into a 120 V
electrical outlet. If the specific heat capacity of water is 4186
J/kgC°, approximately how long does it take to boil all of the water?
a) 5 minutes
b) 8 minutes
c) 10 minutes
d) 13 minutes
e) 15 minutes
35. 20.4.2. The insulated wiring in a house can safely carry a maximum current
of 18 A. The electrical outlets in the house provide an alternating
voltage of 120 V. A space heater when plugged into the outlet operates
at an average power of 1500 W. How many space heaters can safely be
plugged into a single electrical outlet and turned on for an extended
period of time?
a) zero
b) one
c) two
d) three
e) four
36. 20.4.3. A portable CD player was recently introduced that has a
“special power saving technology.” The manufacturer claims
that with only two standard AA batteries (together: 3.0 V, 20 kJ
energy storage) that the player can be played for about 25 hours.
What is the approximate resistance in the CD player’s electrical
circuitry?
a) 41 Ω
b) 0.010 Ω
c) 300 Ω
d) 1.5 Ω
e) 15 Ω
37. 20.4.4. A wire is used as a heating element that has a resistance that is
fairly independent of its temperature within its operating range.
When a current I is applied to the wire, the energy delivered by the
heater each minute is E. For what amount of current will the
energy delivered by the heater each minute be 4E?
a) 2I
b) 4I
c) 0.5I
d) 0.25I
e) 8I
41. In circuits that contain only resistance, the current reverses direction
each time the polarity of the generator reverses.
( ) ( )ftIft
R
V
R
V
I o
o
ππ 2sin2sin ===
peak current
42. ( )ftVIIVP oo π2sin2
==
( )ftII o π2sin= ( )ftVV o π2sin=
45. Example 6 Electrical Power Sent to a
Loudspeaker
A stereo receiver applies a peak voltage of
34 V to a speaker. The speaker behaves
approximately as if it had a resistance of 8.0 Ω.
Determine (a) the rms voltage, (b) the rms
current, and (c) the average power for this
circuit.
47. Conceptual Example 7 Extension Cords and a Potential Fire Hazard
During the winter, many people use portable electric space heaters to keep
warm. Sometimes, however, the heater must be located far from a 120-V wall
receptacle, so an extension cord must be used. However, manufacturers often
warn against using an extension cord. If one must be used, they recommend
a certain wire gauge, or smaller. Why the warning, and why are smaller-gauge
wires better then larger-gauge wires?
48. 20.5.1. The graph shows the current as a function of time for an
electrical device plugged into a outlet with an rms voltage of 120
V. What is the resistance of the device?
a) 24 Ω
b) 21 Ω
c) 17 Ω
d) 14Ω
e) 12 Ω
49. 20.5.2. Consider the circuits shown in parts A and B in the picture. In part A, a light bulb is
plugged into a wall outlet that has an rms voltage of 120 volts. A current I passes through the
circuit and the bulb turns on. In part B, a second, identical light bulb is connected in series in
the circuit. How does the current in circuit B compare with that in circuit A?
a) The current is the same, I, as in part A.
b) The current is twice as much, 2I, as in part A.
c) The current in part B is zero amperes.
d) The current is one fourth as much, 0.25I, as in part A.
e) The current is one half as much, 0.5I, as in part A.
51. Series Wiring
There are many circuits in which more than one device is
connected to a voltage source.
Series wiring means that the devices are connected in
such a way that there is the same electric current
through each device. (One Path)
52. 21 VVV +=
+++= 321 RRRRSSeries resistors
Resistance in a series Circuit
As we will discuss later, the sum of all voltage in a circuit must
equal zero.
Voltage supplied by battery is lost by resistors
21 IRIR += ( )21 RRI += SIR=
∑=
i
iS RR
53. Example 8 Resistors in a Series Circuit
A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series with a 12.0 V
battery. Assuming the battery contributes no resistance to the circuit, find
(a) the current, (b) the power dissipated in each resistor, and (c) the total
power delivered to the resistors by the battery.
(a)
(b)
(c)
Ω=Ω+Ω= 00.900.300.6SR
SR
V
I =
RIP 2
=
RIP 2
=
W31.5W6.10 +=P
Ω
=
00.9
V0.12
A33.1=
( ) ( )Ω= 00.6A33.1
2
W6.10=
( ) ( )Ω= 00.3A33.1
2
W31.5=
W9.15=
54. 20.6.1. Consider the circuit shown in the drawing. Two identical light bulbs, labeled
A and B, are connected in series with a battery and are illuminated equally.
There is a switch in the circuit that is initially open. Which one of the following
statements concerning the two bulbs is true after the switch is closed?
a) Bulbs A and B will be off.
b) Bulbs A and B will be equally
illuminated.
c) Bulb A will be brighter and bulb B
will be off.
d) Bulb A will be off and bulb B
will be brighter.
e) Both bulbs will be dimmer than before the switch was closed.
56. Parallel Wiring
Parallel wiring means that the
devices are connected in such a
way that the same voltage is applied
across each device.
Multiple paths are present.
When two resistors are connected in
parallel, each receives current from the
battery as if the other was not present.
Therefore the two resistors connected
in parallel draw more current than does
either resistor alone.
58. parallel resistors…
+++=
321
1111
RRRRP
Parallel Wiring
As we will discuss later, the total
current flowing into any point must
equal the total current flowing out.
21 III +=
21 R
V
R
V
+=
+=
21
11
RR
V
=
PR
V
1
∑=
i iP RR
11
59. Simplifying Circuits
∑=
i iP RR
11
R1 = 5 Ω
R2 = 3 Ω
21
11
RR
+=
21
21
RR
RR
R
+
=
21
121
RR
RR
R
+
=
( )( )
Ω+Ω
ΩΩ
=
35
35
Ω= 89.1R
0
5
RTotal
OR
60. Example 10 Main and Remote Stereo Speakers
Most receivers allow the user to connect to “remote” speakers in addition
to the main speakers. At the instant represented in the picture, the voltage
across the speakers is 6.00 V. Determine (a) the equivalent resistance
of the two speakers, (b) the total current supplied by the receiver, (c) the
current in each speaker, and (d) the power dissipated in each speaker.
61. (a)
Ω
+
Ω
=
00.4
1
00.8
11
PR
Ω= 67.2
(b)
PR
V
I rms
rms =
R
V
I rms
rms =(c)
R
V
I rms
rms =
(d) rmsrmsVIP =
rmsrmsVIP =
∑=
i iP RR
11
Ω
=
00.8
3
Ω
=
67.2
V00.6
A25.2=
Ω
=
00.8
V00.6
A750.0= A
00.4
V00.6
Ω
= A50.1=
( )( )V00.6A750.0= W50.4=
( )( )V00.6A50.1= W00.9=
62. Conceptual Example 11 A Three-Way Light Bulb
and Parallel Wiring
Within the bulb there are two separate filaments.
When one burns out, the bulb can produce only
one level of illumination, but not the highest.
Are the filaments connected in series or
parallel?
How can two filaments be used to produce three
different illumination levels?
63. 20.7.1. Consider the three resistors and the battery in the circuit
shown. Which resistors, if any, are connected in parallel?
a) R1 and R2
b) R1 and R3
c) R2 and R3
d) R1 and R2 and R3
e) No resistors are connected in parallel.
64. 20.7.2. Consider the circuits shown in parts A and B in the picture. In part A, a
light bulb is plugged into a wall outlet that has an rms voltage of 120 volts. A
current I passes through the circuit and the bulb turns on. In part B, a second,
identical light bulb is connected in parallel in the circuit. How does the total
current in circuit B compare with that in circuit A?
a) The current is the same, I, as in part A.
b) The current is twice as much, 2I, as
in part A.
c) The current in part B is zero amperes.
d) The current is one fourth as much, 0.25I, as in part A.
e) The current is one half as much, 0.5I, as in part A.
65. 20.7.3. Two light bulbs, one “50 W” bulb and one “100 W” bulb, are
connected in parallel with a standard 120 volt ac electrical outlet.
The brightness of a light bulb is directly related to the power it
dissipates. Therefore, the 100 W bulb appears brighter. How does
the brightness of the two bulbs compare when these same bulbs
are connected in series with the same outlet?
a) Both bulbs will be equally bright.
b) The “100 W” bulb will be brighter.
c) The “50 W” bulb will be brighter.
68. 20.8.1. Consider the three identical light bulbs shown in the circuit.
Bulbs B and C are wired in series with each other and are wired in
parallel with bulb A. When the bulbs are connected to the battery as
shown, how does the brightness of each bulb compare to the others?
a) Bulbs B and C are equally bright,
but bulb A is less bright.
b) Bulbs B and C are equally bright,
but less bright than bulb A.
c) All three bulbs are equally bright.
d) Bulbs A and B are equally bright, but bulb C is less bright.
e) Only bulb A is illuminated.
69. 20.8.2. A circuit is formed using a battery, three identical resistors,
and connecting wires as shown. How does the current passing
through R3 compare with that passing through R1?
a) I3 < I1
b) I3 = I1
c) I3 > I1
d) This cannot be determined without knowing the amount of current
passing through R2.
70. 20.8.3. What is the approximate equivalent resistance of the five
resistors shown in the circuit?
a) 21 Ω
b) 7 Ω
c) 11 Ω
d) 14 Ω
e) 19 Ω
78. Internal Resistance
Batteries and generators add some resistance to a circuit.
This resistance is called internal resistance.
The actual voltage between the terminals of a battery is
known as the terminal voltage.
79. Example 12 The Terminal Voltage of a Battery
The car battery has an emf of 12.0 V and an internal
resistance of 0.0100 Ω. What is the terminal voltage when
the current drawn from the battery is (a) 10.0 A and (b)
100.0 A?
(a) IrV =
V10.0V0.12 −
(b) IrV =
V0.1V0.12 −
( )( )Ω= 010.0A0.10 V10.0=
11.9V=
( )( )Ω= 010.0A0.100 V0.1=
11.0V=
80. 20.9.1. In physics lab, two students measured the potential difference
between the terminals of a battery and the current in a circuit connected
to the battery. The students then made a graph of the two parameters as
shown. They then drew a best fit line through the data. From their
results, determine the approximate internal resistance of the battery.
a) 0.002 Ω
b) 0.08 Ω
c) 0.1 Ω
d) 0.3 Ω
e) 0.6 Ω
82. Loop Rule
The loop rule expresses conservation of energy in terms of
the electric potential.
States that for a closed circuit loop, the total of all potential
rises is the same as the total of all potential drops.
83. Junction Rule
Conservation of mass
Electrons entering must equal the
electrons leaving
The junction rule states that the total
current directed into a junction must
equal the total current directed out of
the junction.
84. Example 14 Using Kirchhoff’s Loop Rule
Determine the current in the circuit.
( ) ( )
dropspotentialrisespotential
0.8V0.612V24 Ω++Ω= II
A90.0=I
∑ =
i
iV 0
( )321 VVVVbattery ++=
85. Reasoning Strategy
Applying Kirchhoff’s Rules
1. Draw the current in each branch of the circuit. Choose any
direction. If your choice is incorrect, the value obtained for
the current will turn out to be a negative number.
2. Mark each resistor with a + at one end and a – at the other
end in a way that is consistent with your choice for current
direction in step 1. Outside a battery, conventional current is
always directed from a higher potential (the end marked +) to
a lower potential (the end marked -).
3. Apply the junction rule and the loop rule to the circuit,
obtaining in the process as many independent equations as
there are unknown variables.
4. Solve these equations simultaneously for the unknown
variables.
86. 20.10.1. What is the current through the 4-Ω resistor in this circuit?
a) 0.67 A
b) 0.75 A
c) 1.0 A
d) 1.3 A
e) 1.5 A
87. 20.10.2. What is the current through the 1-Ω resistor in this circuit?
a) 2.8 A
b) 3.0 A
c) 3.4 A
d) 4.3 A
e) 4.8 A
88. 20.10.3. Which one of the following equations is not correct relative
to the other four equations determined by applying Kirchoff’s
Rules to the circuit shown?
a) I2 = I1 + I4
b) I2 = I3 + I5
c) 6 V − (8 Ω) I1 − (5 Ω) I2 − (4 Ω) I3 = 0
d) 6 V − (6 Ω) I4 − (5 Ω) I2 − (2 Ω) I5 = 0
e) 6 V − (8 Ω) I1 − (6 Ω) I4 − 6 V − (2 Ω) I5 − (4 Ω) I3 = 0
90. A dc galvanometer. The coil of
wire and pointer rotate when there
is a current in the wire.
91. An ammeter must be inserted into
a circuit so that the current passes
directly through it.
92. If a galvanometer with a full-scale
limit of 0.100 mA is to be used to
measure the current of 60.0 mA, a
shunt resistance must be used so that
the excess current of 59.9 mA can
detour around the galvanometer coil.
93. To measure the voltage between two points
in a circuit, a voltmeter is connected between
the points.
95. Parallel capacitors
∑=
i
iP CC
21 qqq +=
Capacitors in Parallel
Voltage is the same on each side of the circuit
Charges on each capacitor directly add
VCVC 21 += ( )VCC 21 +=
96. 21 VVV +=
Series capacitors
∑=
i iS CC
11
Capacitors in Series
Since there is only one path, charge is the same in all
capacitors regardless of capacitance
Voltage drop of each capacitor directly add
21 C
q
C
q
+=
+=
21
11
CC
q
97. 20.12.1. A parallel plate capacitor is connected to a battery and becomes fully
charged. A voltmeter is used to measure the potential difference across the
plates of the capacitor. Then, an uncharged thin metal plate is inserted into the
gap between the parallel plates without touching either plate. What affect, if
any, does the insertion of the plate have on the potential difference across the
plates?
a) The potential difference will not change.
b) The potential difference will increase to twice its initial value.
c) The potential difference will decrease to one half its initial value.
d) The potential difference will increase to a value that cannot be determined
without having more information.
e) The potential difference will decrease to a value that cannot be determined
without having more information.
98. 20.12.2. Three parallel plate capacitors, each having a capacitance of
1.0 µF are connected in series. The potential difference across
the combination is 100 V. What is the charge on any one of the
capacitors?
a) 30 µC
b) 300 µC
c) 3000 µC
d) 100 µC
e) 1000 µC
103. 20.13.1. In physics lab, Rebecca measured the voltage across an
unknown capacitor in an RC circuit, every ten seconds after a
switch in the circuit that allows the capacitor to discharge is
closed. The capacitor was initially fully charged. Using the
graph, estimate the time constant.
a) 7.5 s
b) 15 s
c) 30 s
d) 45 s
e) 60 s
104. 20.13.2. An RC circuit contains a battery, a switch, a resistor, and a
capacitor – all connected in series. Initially, the switch is open and the
capacitor is uncharged. Which one of the following statements
correctly describes the current in the circuit during the time the
capacitor is charging?
a) The current is increasing with increasing time.
b) The current is constant with increasing time.
c) The current is decreasing with increasing time.
d) The current increases for the first half of the time until the capacitor is
fully discharged, and then decreases during the second half of the time.
e) The current can either increase or decrease with increasing time
depending on the value of the time constant.