Electrical Engineering: Principles & Applications (7th Edition)
7th Edition
ISBN: 9780134484143
Author: Allan R. Hambley
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 4.38P
For the circuit shown in Figure P4.38,, find an expression for the current
Figure P4.38
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Consider the circuit shown in Figure P4.18. Prior to t=0, v 1 =100 V, and v 2 =0.a. Immediately after the switch is closed, what is the value of the current [i.e., what is thevalue of i( 0+ ) ]?b. Write the KVL equation for the circuit in terms of the current and initial voltages. Take thederivative to obtain a differential equation.c. What is the value of the time constant in this circuit?d. Find an expression for the current as a function of time.e. Find the value that v2 approaches as t becomes very large.
Consider the circuit shown in Figure P4.54. a. Write the differential equation for i(t). b. Find the time constant and the form of the complementary solution. c. Usually, for an exponential forcing function like this, we would try a particular solution of the form ip(t)=K exp (−3t). Why doesn’t that work in this case? d. Find the particular solution. [Hint: Try a particular solution of the form ip(t)=K t exp(−3t).] e. Find the complete solution for i(t).
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Chapter 4 Solutions
Electrical Engineering: Principles & Applications (7th Edition)
Ch. 4 - Suppose we have a capacitance C discharging...Ch. 4 - The dielectric materials used in real capacitors...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - A 100F capacitance is initially charged to 1000 V....Ch. 4 - At t = 0, a charged 10{ F capacitance is connected...Ch. 4 - At time t1 , a capacitance C is charged to a...Ch. 4 - Given an initially charged capacitance that begins...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - In physics, the half-life is often used to...Ch. 4 - We know that a 50F capacitance is charged to an...
Ch. 4 - We know that the capacitor shown in Figure P4.11...Ch. 4 - The purchasing power P of a certain unit of...Ch. 4 - Derive an expression for vC(t) in the circuit of...Ch. 4 - Suppose that at t= 0, we connect an uncharged 10 F...Ch. 4 - Suppose we have a capacitance C that is charged to...Ch. 4 - A person shuffling across a dry carpet can be...Ch. 4 - Prob. 4.17PCh. 4 - Consider the circuit shown in Figure P4.18. Prior...Ch. 4 - List the steps for dc steady-state analysis of RLC...Ch. 4 - Explain why we replace capacitances with open...Ch. 4 - Solve for the steady-state values of i1, i2, and...Ch. 4 - Consider the circuit shown in Figure P4.22. What...Ch. 4 - In the circuit of Figure P4.23, the switch is in...Ch. 4 - The circuit shown in Figure P4.24 has been set up...Ch. 4 - Solve for the steady-state values of i1 , i2, i3,...Ch. 4 - The circuit shown in Figure P4.26 is operating in...Ch. 4 - Prob. 4.27PCh. 4 - Consider the circuit of Figure P4.28 in which the...Ch. 4 - For the circuit shown in Figure P4.29, the switch...Ch. 4 - Consider the circuit of Figure P4.30 in which the...Ch. 4 - Give the expression for the time constant of a...Ch. 4 - A circuit consists of switches that open or close...Ch. 4 - The circuit shown in Figure P4.33 is operating in...Ch. 4 - Consider the circuit shown in Figure P4.34. The...Ch. 4 - Repeat Problem P4.34 given iL(0)=0A .Ch. 4 - Real inductors have series resistance associated...Ch. 4 - Determine expressions for and sketch is(t) to...Ch. 4 - For the circuit shown in Figure P4.38,, find an...Ch. 4 - The circuit shown in Figure P4.39 is operating in...Ch. 4 - Consider the circuit shown in Figure P4.40. A...Ch. 4 - Due to components not shown in the figure, the...Ch. 4 - The switch shown in Figure P4.42 has been closed...Ch. 4 - Determine expressions for and sketch vR(t) to...Ch. 4 - What are the steps in solving a circuit having a...Ch. 4 - Prob. 4.45PCh. 4 - Solve for vC(t) for t > 0 in the circuit of Figure...Ch. 4 - Solve for v(t) for t > 0 in the circuit of Figure...Ch. 4 - Prob. 4.48PCh. 4 - Consider the circuit shown inFigure P4.49. The...Ch. 4 - Consider the circuit shown in Figure P4.50. The...Ch. 4 - The voltage source shown in Figure P4.51 is called...Ch. 4 - Determine the form of the particular solution for...Ch. 4 - Determine the form of the particular solution for...Ch. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - How can first-or second-order circuits be...Ch. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Sketch a step response for a second-order system...Ch. 4 - A dc source is connected to a series RLC circuit...Ch. 4 - Repeat Problem P4.61 for R = 40 .Ch. 4 - Repeat Problem P4.61 for R = 20 .Ch. 4 - Prob. 4.64PCh. 4 - Repeat Problem P4.64 for R=50 .Ch. 4 - Repeat Problem P4.64 for R=500 .Ch. 4 - Solve for i(t) for t > 0 in the circuit of Figure...Ch. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Prob. 4.70PCh. 4 - Use MATLAB to derive an expression for vc(t)in the...Ch. 4 - Prob. 4.72PCh. 4 - Consider the circuit shown in FigureP4.50 in which...Ch. 4 - Prob. 4.74PCh. 4 - Prob. 4.75PCh. 4 - Use MATLAB to solve for the mesh currents in the...Ch. 4 - The switch m the circuit shown in Figure T4.1 is...Ch. 4 - Prob. 4.2PTCh. 4 - Consider the circuit shown in Figure T4.3. Figure...Ch. 4 - Consider the circuit shown in Figure T4.4 in which...Ch. 4 - Write the MATLAB commands to obtain the solution...
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- Derive an expression for vC(t) in the circuit of Figure P4.13 and sketch vC(t) to scale versus timearrow_forwardConsider the circuit shown in Figure P4.55. a. Write the differential equation for v(t).b. Find the time constant and the form of the complementary solution.c. Usually, for an exponential forcing function like this, we would try a particular solution ofthe form vp(t) = K exp (−10t). Why doesn’t that work in this case?d. Find the particular solution. [Hint: Try a particular solution of the form vp(t)=K t exp (−10t). How ]e. Find the complete solution for v(t).arrow_forwardAn electromagnet can be modeled as an inductor in series with a resistor. Consider a large electromagnet of inductance L = 14.5 H and resistance R = 5.50 connected to a 24.0-V battery and switch as in the figure shown below. After the switch is closed, find the following. @ (a) the maximum current carried by the electromagnet 4.36 A (b) the time constant of the circuit 2.63 ✔S (c) the time it takes the current to reach 95.0% of its maximum value. 0.132 x Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. starrow_forward
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- A controlled rectifier circuit is generating thewaveform of Figure P4.30 starting from a sinusoidalvoltage of 110 V rms. Find the angle θthat corresponds to delivering exactly one-half of thetotal available power in the waveform to a resistiveload.arrow_forwardPls help need asap...explain as you solve plsarrow_forwardThe capacitor model we have used so far has beentreated as an ideal circuit element. A more accuratemodel for a capacitor is shown in Figure P4.67. Theideal capacitor, C, has a large “leakage” resistance, RC,in parallel with it. RC models the leakage currentthrough the capacitor. R1 and R2 represent the leadwire resistances, and L1 and L2 represent the lead wireinductances.a. If C = 1 μF, RC = 100 MΩ, R1 = R2 = 1 μΩ andL1 = L2 = 0.1 μH, find the equivalent impedanceseen at the terminals a and b as a function offrequency ω.b. Find the range of frequencies for which Zab iscapacitive, i.e., Xab > 10|Rab.Hint: Assume that RC is is much greater than 1/wC so thatyou can replace RC by an infinite resistance in part b.arrow_forward
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