Principles and Applications of Electrical Engineering
6th Edition
ISBN: 9780073529592
Author: Giorgio Rizzoni Professor of Mechanical Engineering, James A. Kearns Dr.
Publisher: McGraw-Hill Education
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Chapter 4, Problem 4.56HP
To determine
Thevalue of current
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The circuit shown in Figure P4.26 is operating in steady state. Determine the values of i L,v x ,and v C .
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The circuit shown in Figure P4.39 is operating in steady state with the switch closed prior to t=0. Find expressions for i L ( t ) for t<0 and for t≥0. Sketch iL(t) to scale versus time
Chapter 4 Solutions
Principles and Applications of Electrical Engineering
Ch. 4 - The current through a 0.8-H inductor is given by...Ch. 4 - For each case shown below, derive the expression...Ch. 4 - Derive the expression for the voltage across...Ch. 4 - In the circuit shown in Figure P4.4, assume R=1...Ch. 4 - Prob. 4.5HPCh. 4 - In the circuit shown in Figure P4.4, assume R=2...Ch. 4 - In the circuit shown in Figure P4.7, assume R=2...Ch. 4 - Prob. 4.8HPCh. 4 - Prob. 4.9HPCh. 4 - Prob. 4.10HP
Ch. 4 - The voltage waveform shown in Figure P4.10 is...Ch. 4 - The voltage across a 0.5-mH inductor, Plotted as a...Ch. 4 - Prob. 4.13HPCh. 4 - The current through a 16-H inductor is zero at t=0...Ch. 4 - The voltage across a generic element X has the...Ch. 4 - The plots shown in Figure P4.16 are the voltage...Ch. 4 - The plots shown in Figure P4.17 are the voltage...Ch. 4 - The plots shown in Figure P4.18 are the voltage...Ch. 4 - The plots shown in Figure P4.19 are the voltage...Ch. 4 - The voltage vL(t) across a 10-mH inductor is shown...Ch. 4 - The current through a 2-H inductor is p1otted in...Ch. 4 - Prob. 4.22HPCh. 4 - Prob. 4.23HPCh. 4 - Prob. 4.24HPCh. 4 - The voltage vC(t) across a capacitor is shown in...Ch. 4 - The voltage vL(t) across an inductor is shown in...Ch. 4 - Find the average and rms values of x(t) when:...Ch. 4 - The output voltage waveform of a controlled...Ch. 4 - Refer to Problem 4.28 and find the angle + that...Ch. 4 - Find the ratio between the average and rms value...Ch. 4 - The current through a 1- resistor is shown in...Ch. 4 - Derive the ratio between the average and rms value...Ch. 4 - Find the rms value of the current waveform shown...Ch. 4 - Determine the rms (or effective) value of...Ch. 4 - Assume steady-state conditions and find the energy...Ch. 4 - Assume steady-state conditions and find the energy...Ch. 4 - Find the phasor form of the following functions:...Ch. 4 - Convert the following complex numbers to...Ch. 4 - Convert the rectangular factors to polar form and...Ch. 4 - Complete the following exercises in complex...Ch. 4 - Convert the following expressions to rectangular...Ch. 4 - Find v(t)=v1(t)+v2(t) where...Ch. 4 - The current through and the voltage across a...Ch. 4 - Express the sinusoidal waveform shown in Figure...Ch. 4 - Prob. 4.45HPCh. 4 - Convert the following pairs of voltage and current...Ch. 4 - Determine the equivalent impedance seen by the...Ch. 4 - Determine the equivalent impedance seen by the...Ch. 4 - The generalized version of Ohm’s law for impedance...Ch. 4 - Prob. 4.50HPCh. 4 - Determine the voltage v2(t) across R2 in the...Ch. 4 - Determine the frequency so that the current Ii...Ch. 4 - Prob. 4.53HPCh. 4 - Use phasor techniques to solve for the current...Ch. 4 - Use phasor techniques to solve for the voltage...Ch. 4 - Prob. 4.56HPCh. 4 - Solve for VR shown in Figure P4.57. Assume:...Ch. 4 - With reference to Problem 4.55, find the value of ...Ch. 4 - Find the current iR(t) through the resistor shown...Ch. 4 - Find vout(t) shown in Figure P4.60.Ch. 4 - Find the impedance Z shown in Figure...Ch. 4 - Find the sinusoidal steady-state output vout(t)...Ch. 4 - Determine the voltage vL(t) across the inductor...Ch. 4 - Determine the current iR(t) through the resistor...Ch. 4 - Find the frequency that causes the equivalent...Ch. 4 - a. Find the equivalent impedance Zo seen by the...Ch. 4 - A common model for a practical capacitor has...Ch. 4 - Using phasor techniques, solve for vR2 shown in...Ch. 4 - Using phasor techniques to solve for iL in the...Ch. 4 - Determine the Thévenin equivalent network seen by...Ch. 4 - Determine the Norton equivalent network seen by...Ch. 4 - Use phasor techniques to solve for iL(t) in...Ch. 4 - Use mesh analysis to determine the currents i1(t)...Ch. 4 - Prob. 4.74HPCh. 4 - Prob. 4.75HPCh. 4 - Find the Thévenin equivalent network seen by the...Ch. 4 - Prob. 4.77HPCh. 4 - Prob. 4.78HPCh. 4 - Prob. 4.79HPCh. 4 - Prob. 4.80HPCh. 4 - Use mesh analysis to find the phasor mesh current...Ch. 4 - Write the node equations required to solve for all...Ch. 4 - Determine Vo in the circuit of Figure...Ch. 4 - Prob. 4.84HP
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Similar questions
- Consider 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_forwardConsider the circuit of Figure P4.17, in which the switch instantaneously moves back and forth between contacts A and B, spending 2 seconds in each position. Thus, the capacitor repeatedly charges for 2 seconds and then discharges for 2 seconds. Assume that v C ( 0 )=0 and that the switch moves to position A at t=0. Determine v C ( 2 ), v C ( 4 ), v C ( 6 ), and v C ( 8 ).arrow_forwarda. Find the equivalent impedance ZL shown inFigure P4.66(a), as seen by the source, if thefrequency is 377 rad/s.b. If we wanted the source to see the load ascompletely resistive, what value of capacitanceshould we place between the terminals a and b asshown in Figure P4.66(b)? Hint: Find an expressionfor the equivalent impedance ZL, and then find C sothat the phase angle of the impedance is zero.arrow_forward
- 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).arrow_forwardDue to components not shown in the figure, the circuit of Figure P4.41 has i L ( 0 )= I i . a. Write an expression for i L (t) for t≥0. b. Find an expression for the power delivered to the resistance as a function of time. c. Integrate the power delivered to the resistance from t=0 to t=∞, and show that the result is equal to the initial energy stored in the inductancearrow_forwardSolve for i L ( t ) for t>0 in the circuit of Figure P4.48. You will need to make an educated guess as to the form of the particular solution. [Hint: The particular solution includes terms with the same functional forms as the terms found in the forcing function and its derivatives.]arrow_forward
- Find the transmission parameter for the network shown in Figure Q4(b).arrow_forwardConsider 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.arrow_forwardSolve for i(t) for t>0 in the circuit of Figure P4.67, with R=200 Ω, given that i( 0+ )=0 and v C ( 0+ )=20 V [Hint: Try a particular solution of the form i p ( t )= A cos( 100t )+B sin( 100t ).]arrow_forward
- The 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_forwardConsider the circuit shown in Figure T4.3.a. Write the differential equation for i(t). b. Find the time constant and the form of the complementary solution. c. Find the particular solution. d. Find the complete solution for i(t).arrow_forwardThe coil resistor in series with L models the internallosses of an inductor in the circuit of Figure P4.53.Determine the current supplied by the source ifvs(t) = Vo cos(ωt + 0)Vo = 10 V, ω = 6 M rad/s, Rs = 50 Rc = 40 L = 20 μH C = 1.25 nFarrow_forward
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