Chapter 8: The Complete Response of RL and RC Circuits ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 8 The Complete

Chapter 8: The Complete Response of RL and RC Circuits

©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed

Chapter 8

The Complete Response of RL and RC Circuits



Figure 8.0-1A plan for analyzing first-order circuits. (a) First, separate the energy storage elements from the rest of the circuit. (b) Next, replace the circuit connected to a capacitor by its Thévenin equivalent circuit, or replace the circuit connected to an inductor by its Norton equivalent circuit.



Figure 8.0-2(a) A circuit and (b) its complete response.



Figure 8.1-1(a) A printer connected to a laptop computer. (b) Two circuits connected by a cable and (c) an equivalent circuit.



Figure 8.1-2Voltages that occur during a transition from a logic 0 to a logic 1.



Figure 8.2-1Common forms of electrical signals shown on the screen of an oscilloscope. Courtesy of Panasonic Industrial Co.



Figure 8.2-2(a) An analog signal and the corresponding sampled signal. (b) A digital signal obtained by encoding the sampled signal.



Figure 8.2-3(a) A signal is sent from the transmitter to the receiver using a cable. (b) The cable is modeled as a first-order circuit.



Figure 8.3-1(a) A first-order circuit containing a capacitor. (b) After the switch closes, the circuit connected to the capacitor is replaced by its Thévenin equivalent circuit.



Figure 8.3-2(a) A first-order circuit containing an inductor. (b) After the switch closes, the circuit connected to the inductor is replaced by its Norton equivalent circuit.



Figure 8.3-3A graphical technique for measuring the time constant of a first-order circuit.



Figure 8.3-4(a) A first-order circuit and (b) an equivalent circuit that is valid after the switch opens. (c) A plot of the complete response, v(t), given in Eq. 8.3-8.



Figure 8.3-5(a) A first-order circuit and (b) an equivalent circuit that is valid after the switch closes. (c) A plot of the complete response, i(t), given by Eq.8-3-9.



Figure 8.3-6(a) A first-order circuit. The equivalent circuit for (b) t 0 and (c) t 0.



Figure 8.3-7(a) A first-order circuit. The equivalent circuit for (b) t 0 and (c) t 0.



Figure 8.3-8(a) A first-order circuit, (b) the circuit after the switch opens, and (c) the equivalent circuit after the switch opens.



Figure E 8.3-1



Figure E 8.3-2



Figure E 8.3-3



Figure E 8.3-4



Figure E 8.3-5



Figure E 8.3-6



Figure 8.4-1(a) A circuit with sequential switching. (b) The equivalent circuit before t 0. (c) The equivalent circuit for 0 t l ms. (d) The equivalent circuit after t 1 ms.



Figure 8.4-2Current waveform for t 0. The exponential has a different time constant for 0 t t1 and for t t1 where t1 1 ms.



Figure 8.4-3A comparator.



Figure 8.4-4A comparator is used to compare the capacitor voltage, vc (t), to a threshold voltage, VT.



Figure 8.4-5The initial capacitor voltage is vc(0) 1.667 volts, and the comparator output is to switch from VL 0 to VH 5 volts at time t1 1 ms.



Figure 8.4-6A comparator is used to compare the resistor voltage, vR(t), to a threshold voltage, VT.



Figure E 8.4-1



Figure E 8.4-2



Figure 8.5-1(a) A first-order circuit containing a dependent source. (b) The circuit used to calculate the initial condition. (c) The circuit used to calculate Voc. (d) The circuit used to calculate RTH.



Figure 8.5-2(a) A first order circuit containing a dependent source. (b) The circuit used to calculate the Thévenin resistance of the part of the circuit connected to the capacitor.



Figure 8.6-1Application of a constant-voltage source at t t0 using two switches both acting at t t0.



Figure 8.6-2Unit step forcing function. u(t t0).



Figure 8.6-3Single-switch equivalent circuit for the step voltage source.



Figure 8.6-4Symbol for the step voltage source of magnitude V0 applied at t t0.



Figure 8.6-5(a) Rectangular voltage pulse. (b) Two-step voltage waveforms that yield the voltage pulse.



Figure 8.6-6Two-step voltage sources that yield a rectangular voltage pulse, v(t) with a magnitude of V0 and a duration of (t1 t0) where t0 t1.



Figure 8.6-7Pulse source connected to an RL circuit. The pulse is generated by the combination of two-step voltage sources each with units in volts.



Figure 8.6-8Response of the RL circuit shown in Figure 8.6-7.



Figure E 8.6-1



Figure E 8.6-2



Figure E 8.6-3



Figure 8.7-1(a) A circuit with a nonconstant source, (b) the appropriate equivalent circuit after the switch opens; and (c) the appropriate equivalent circuit before the switch opens.



Figure 8.7-2(a) A circuit with a nonconstant source. (b) The equivalent circuit for t 0.



Figure E 8.7-1(a) The NASA space station design shows the longer habitable modules that would house an orbiting scientific laboratory. (b) The circuit for energy storage for the laboratories. Photograph courtesy of the National Aeronautics and Space Administration.



Figure E 8.7-2



Figure E 8.7-3



Figure 8.8-1(a) A first-order circuit with a sinusoidal input and (b) a plot of its complete response produced using MATLAB.



Figure 8.9-1(a) An RC circuit. (b) The circuit redrawn for Pspice. (c) The Pspice input file.



Figure 8.9-2Complete responses, v(t), of the RC circuit.



Figure 8.10-1(a) A transient response and (b) the corresponding circuit.



Figure 8.10-2Circuits used to calculate the (a) initial voltage, (b) final voltage, and (c) time constant.



Figure 8.10-3Interpretation of the transient response.



Figure 8.10-4(a) A transient response and (b) the corresponding circuit.



Figure 8.10-5Circuits used to calculate (a) the steady-state voltage when the switch is open, (b) the steady-state voltage when the switch is closed, (c) the time constant when the switch is open, and (d) the time constant when the switch is closed.



Figure 8.10-6Interpretation of the transient response.



Figure 8.11-1(a) A printer connected to a laptop computer. (b) Two circuits connected by a cable and (c) an equivalent circuit.



Figure 8.11-2Voltages that occur during a transition from a logic 0 to a logic 1.

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Chapter 8: The Complete Response of RL and RC Circuits ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 8 The Complete