Lect07 handout
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1) RC circuits involve resistors and capacitors. Charging and discharging of capacitors in such circuits does not occur instantaneously due to the presence of resistors. 2) The time constant, τ, of an RC circuit is equal to RC. It represents the time required for a capacitor's charge or voltage to change by approximately 63.2% of its maximum or initial value. 3) In the long run, the current through a charged capacitor becomes zero as it reaches its maximum charge, acting as an open circuit. For a discharging capacitor, the current becomes zero as its charge reduces to zero.
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Lect07 handout
1) RC circuits involve resistors and capacitors. Charging and discharging of capacitors in such circuits does not occur instantaneously due to the presence of resistors.
2) The time constant, τ, of an RC circuit is equal to RC. It represents the time required for a capacitor's charge or voltage to change by approximately 63.2% of its maximum or initial value.
3) In the long run, the current through a charged capacitor becomes zero as it reaches its maximum charge, acting as an open circuit. For a discharging capacitor, the current becomes zero as its charge reduces to zero.
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Lect07 handout
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2) The time constant, τ, of an RC circuit is equal to RC. It represents the time required for a capacitor's charge or voltage to change by approximately 63.2% of its maximum or initial value.
3) In the long run, the current through a charged capacitor becomes zero as it reaches its maximum charge, acting as an open circuit. For a discharging capacitor, the current becomes zero as its charge reduces to zero.
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1) Initial conditions refer to the state of a circuit at time t=0+, just after a switch is operated, while final conditions refer to the steady state as t approaches infinity.
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Kirchhoff's rules and rc circuits
1. An RC circuit consists of a resistor and capacitor connected in series or parallel. When a voltage is applied across the circuit, the capacitor will charge up over time through the resistor according to the time constant of the circuit, which is equal to RC.
2. Kirchhoff's laws can be applied to the RC circuit to derive differential equations describing how the current and charge on the capacitor change over time during the charging and discharging processes. The solutions to these equations show that the current and charge decay exponentially with the time constant RC.
3. An oscilloscope can be used to observe the input voltage waveform and voltage across the capacitor to understand the capacitor's charging and discharging behavior in response to
Current Electricity 4 Aug.pdf
This document discusses RC circuits and the behavior of charge and voltage over time in RC circuits. It includes:
1. Explanations of charge, current, and voltage in RC circuits at times t=0, t=∞, and t=time constant.
2. Formulas for charge, current, voltage across resistor and capacitor.
3. Graphs showing growth/decay of charge over time and voltage over time.
4. Examples of calculating charge, current, time constant, and half time for given RC circuits.
Circuits
This lecture covered first-order circuits and their transient responses. Key points:
1) First-order circuits contain resistors and one energy storage element (inductor or capacitor) and their behavior is described by first-order differential equations.
2) The natural response of RL and RC circuits is exponential, with a characteristic time constant.
3) When a step change is applied, voltages and currents will change exponentially from their initial to final values over time.
4) Digital circuits can be modeled as RC circuits, where rise and fall times are determined by the time constant.
Capacitor
This document describes the charging and discharging of a capacitor in an RC circuit. It defines key concepts like the capacitor, resistor, time constant (RC), and charging/discharging curves. The time for a capacitor to charge to 63% or discharge to 37% of the supply voltage is defined as 1 time constant (1RC). Examples calculate the time constant for given circuits and determine voltage values at specific time constants. The document concludes the designed charging/discharging circuit works according to the calculations and lists sources of error and precautions to consider.
Transient response of RC , RL circuits with step input
The document discusses the transient response of RC and RL circuits to step inputs. It defines the natural and forced responses, and derives equations for the total response as the sum of the two. The total response is an exponential decay from the initial voltage/current to the final steady state value. Cut-off frequency is defined as the frequency at which the gain is 0.707. RC and CR circuits can act as low-pass and high-pass filters respectively, with gain determined by frequency relative to cut-off frequency.
Charging C
This document discusses charging and discharging capacitors in circuits. When a capacitor is charging, current flows through the circuit and decreases over time as charge builds up on the capacitor. The time it takes for the charge to reach 63% of its final value is called the time constant, represented by τ, which equals the resistance R multiplied by the capacitance C. When discharging, the current direction reverses but also decreases over time as the stored charge depletes from the capacitor. The energy stored in the capacitor is 1/2 CV^2 and equals the work done by the battery during charging.
Rc and rl circuits
Here are the solutions to the seatwork problems:
1. (a) 10,000 rad/s
(b) 20 V
2. 2.608 μF
3. (a) 134.8 Hz
(b) 119 μC
(c) 0.101 A
4. 200√2 cos(2π100t) Volts
5. (a) 193 ohms
(b) 145 ohms
Thyristor Characteristics, Two Transistor Model Of Thyristor & Thyrisror Turn...
Thyristor Characteristics, Two Transistor Model Of Thyristor & Thyrisror Turn...University of Gujrat, Pakistan
this is all about engineering thyristor is a very important in engineering specially in electrical and electronics engineering.AC Circuit Theory
1) The document discusses LC circuits, noting a qualitative difference in how currents develop in RC versus LC circuits. In an LC circuit, energy can be stored in both the inductor and capacitor without dissipation, unlike an RC circuit where energy is dissipated in the resistor.
2) An LC circuit with an initially charged capacitor will undergo oscillations of the current, not exponential decay as in an RC circuit. The frequency of these oscillations is determined to be 1/sqrt(LC) from the equations for the energy stored in each component.
3) Increasing the inductance decreases the oscillation frequency in an LC circuit, while increasing the capacitance also decreases the frequency, according to the governing equation relating the
Sesión de Laboratorio 3: Leyes de Kirchhoff, Circuitos RC y Diodos
Laboratory session in Physics II subject for September 2016-January 2017 semester in Yachay Tech University (Ecuador). Topic covered: electricity, electrical circuits, resistances, capacitances, diodes
Based on Bruna Regalado's work
B.Sc. Sem II Network theorems
1. The document discusses several important network theorems including Kirchhoff's laws, Thevenin's theorem, maximum power transfer theorem, superposition theorem, and the growth and decay of charge and current in RC and LR circuits respectively.
2. Kirchhoff's laws include Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL states the sum of currents at a node is zero, and KVL states the algebraic sum of voltages in a closed loop is zero.
3. Thevenin's theorem states any linear network can be reduced to a single voltage source in series with a resistance, with the Thevenin voltage and resistance values defined.
Sheet1resistance of resistorTime Constant = 5.3s10v from power sup.docx
Sheet1resistance of resistorTime Constant = 5.3s10v from power supply 54.37 kohmscapacitor 96.9 micro farradsY axistheoretical max 183.9 micro amps0835-0.7955515238536.610-1.61434389121016.215-2.4293808894157.8520-3.1538785998203.3925-3.9935622102251.8330-4.6100761648300.8635-5.3652150213350.4640-5.9909209211400.2545-6.6006864927450.18950-6.8804003955500.13355-7.2317982824550.10160-7.507026893860micro ampsseconds
5 10 15 20 25 30 35 40 45 50 55 60 -0.79555152381367755 -1.6143438912029549 -2.4293808893719371 -3.1538785998159584 -3.9935622102179167 -4.6100761647569461 -5.3652150213448593 -5.9909209211092715 -6.6006864927301665 -6.8804003955327699 -7.2317982823706588 -7.5070268937511528
Sheet285.5k ohms96.9 micro farrads10v from power supplyTime constant = 8.3Y axistheoretical max 117 micro amps050.18-0.8481529267823.616-1.60092722281611.324-2.3373712091244.8432-3.1852592141322.3440-3.9120230054401.1448-4.6311456724480.53456-5.3895333748560.31464-5.9205362279640.2172-6.3228216831720.14880-6.67271694800.12488-6.8496476482880.10896-6.987797986796micro ampsseconds
8 16 24 32 40 48 56 64 72 80 88 96 -0.84815292670693698 -1.6009272227661917 -2.3373712090794614 -3.185259214069216 -3.912023005428146 -4.6311456723913524 -5.3895333748196981 -5.92053622787164 -6.3228216830624246 -6.6727169400157784 -6.8496476481748561 -6.9877979866556732
Sheet384.37k ohms96.9 micro farradstime constant 5.310vx axisy axis4.855-0.66358837837.7410-1.48722027978.9815-2.28278246579.520-2.99573227369.7625-3.7297014486voltsseconds
5 10 15 20 25 -0.6635883783184009 -1.4872202797098513 -2.2827824656978661 -2.99573227355399 -3.7297014486341906
Sheet4resistance 85.5k ohm96.9 micro farradtime constant = 8.3s10vx axisy axis5.348-0.76356964497.8916-1.55589714559.0624-2.36446049679.5432-3.07911388259.7640-3.7297014486voltsseconds
8 16 24 32 40 seconds -0.76356964485649126 -1.5558971455060702 -2.3644604967121334 -3.0791138824930413 -3.7297014486341906
R-C Circuits
Purpose: This lab will consider another electrical component with unique characteristics, the capacitor. The lab will also provide practice constructing and interpreting graphs for the purpose of circuit analysis.
Introduction: As you have learned, a capacitor in its simplest form is two parallel plates of conductive material, separated by a non-conductive material that prevents the plates from touching. Capacitance, “C”, is measured in Farads (F), with typical values of capacitors being measured in μF. Capacitor labeling sometimes deviates from standard metric prefixes in that an upper case “M” is often used in place of the μ symbol for micro- (x 10-6). Do not confuse it with mega- (x 10+6). A mega-Farad capacitor would be enormous, if one could even be built!
As an electrical potential (voltage) is placed across the capacitor, electrical charge flows (current) from the voltage source and builds up on the plates of the capacitor. If connected to a DC source, the current will continue to fl.
Introduction to scr thyristers
The document discusses thyristor characteristics and operation. It begins by describing the thyristor structure as a four layer p-n-p-n semiconductor device with three p-n junctions. It then covers thyristor operation in the forward blocking/off state and at the forward breakdown voltage. Various thyristor triggering methods like gate, thermal, and dv/dt triggering are explained. Thyristor turn-off methods including natural and forced commutation are also summarized. Key thyristor parameters like latching current, holding current, and maximum gate voltages and currents are defined.
PP+for+Ch+31.pdf
1. The document discusses inductance and inductors. It defines inductance and describes how inductors can store current similarly to how containers store water.
2. Charging an inductor involves current building up over time in the inductor, analogous to filling a water container. The rate of current increase decreases as it approaches the maximum steady-state current, following an exponential curve.
3. RL circuits for charging and discharging an inductor are mathematically equivalent to RC circuits. Both involve an exponential curve defined by a common time constant τ, where τ is the time required to reach 63% of the final value.
Lesson 2 Capacitors
A capacitor stores electric charge by having two conductors separated by an insulator. Common applications include computer memory, camera flashes, and surge protectors. The amount of charge stored is proportional to the potential difference between the plates. When a dielectric is placed between the plates, it increases the capacitance by a factor called the dielectric constant. Energy is stored in a capacitor as 1/2 CV^2 and is released when the capacitor discharges through a circuit.
First order circuits
- The document discusses first-order RC and RL circuits.
- Key aspects include: RC and RL circuits can be modeled with first-order differential equations; the natural response of source-free circuits decays exponentially with a time constant τ equal to RC or L/R.
- The energy initially stored in the capacitor or inductor is dissipated in the resistor over time according to an exponential function with the same time constant.
Initial and final condition for circuit
Initial and final condition for circuit
Explain the transient response of a RC circuit
As the capacitor stores energy when there is:
a transition in a unit step function source, u(t-to)
or a voltage or current source is switched into the circuit.
Explain the transient response of a RL circuit
As the inductor stores energy when there is:
a transition in a unit step function source, u(t-to)
or a voltage or current source is switched into the circuit.
RC Circuit
RL Circuit
Circuits
Capacitors and inductors are passive circuit elements that can store energy.
- Capacitors store energy in an electric field between conducting plates separated by an insulator. The capacitance is affected by the area of the plates, distance between plates, and the material between the plates.
- Inductors store energy in a magnetic field created by current through a coil of wire. The inductance depends on the number of wire turns, length of the coil, and material inside the coil.
- Capacitors and inductors have characteristic equations relating voltage, current, charge, and energy that make them useful for circuit analysis. Their properties allow them to be combined in series and parallel configurations.
Assignmentl3 solutions
This document contains solutions to tutorial exercises on electronics circuits involving capacitors and other circuit elements. The first exercise involves determining currents and equivalent capacitance in a circuit with two capacitors. The second involves calculating capacitor voltage over time when a switch changes positions. The third determines capacitor voltage over time for virtually parallel capacitors driven by a voltage source. Subsequent exercises involve determining voltages, currents, and impedances in various RC, RL, and RLC circuits.
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Transient response of RC , RL circuits with step input
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Sesión de Laboratorio 3: Leyes de Kirchhoff, Circuitos RC y Diodos
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Sheet1resistance of resistorTime Constant = 5.3s10v from power sup.docx
Sheet1resistance of resistorTime Constant = 5.3s10v from power sup.docx
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Lect07 handout
- 1. RC Circuits Physics 102: Lecture 7
- 20. Practice! Calculate current immediately after switch is closed: Calculate current after switch has been closed for 0.5 seconds: Calculate current after switch has been closed for a long time: Calculate charge on capacitor after switch has been closed for a long time: Example E – I 0 R – q 0 /C = 0 + + + - - - E – I 0 R – 0 = 0 I 0 = E /R After a long time current through capacitor is zero! E – IR – q ∞ /C = 0 E – 0 – q ∞ /C = 0 q ∞ = E C R C ε S 1 R=10 C=30 mF ε =20 Volts I
- 23. RC Summary Charging Discharging q(t) = q (1-e -t/RC ) q(t) = q 0 e -t/RC V(t) = V (1-e -t/RC ) V(t) = V 0 e -t/RC I(t) = I 0 e -t/RC I(t) = I 0 e -t/RC Short term: Charge doesn’t change (often zero or max) Long term: Current through capacitor is zero. Time Constant = RC Large means long time to charge/discharge
Editor's Notes
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- Initial current through battery. Final current; final voltage across C.
- Initial current through battery. Final current; final voltage across C.
- Initial current through battery. Final current; final voltage across C.
- Followup…what is current a long time later? What is charge on capacitor a long time later?