Electrical Engineering: Principles & Applications (7th Edition)
7th Edition
ISBN: 9780134484143
Author: Allan R. Hambley
Publisher: PEARSON
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Question
Chapter 4, Problem 4.55P
To determine
(a)
The differential equation for
To determine
(b)
The time constant and the form of the complementary solution.
To determine
(c)
Whether the particular solution of the form
To determine
(d)
The particular solution of the differential equation.
To determine
(e)
The complete solution for the equation.
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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).
P4.45.) Write the differential equation for i(t) and
find the complete solution for the circuit of
Figure P4.45. [Hint: Try a particular solution
of the form ip (t) = Ae- ]with out Lapluce
t = 0
10 H
i(t)
5e
Figure P4.45
Consider the circuit shown in Figure P4.70. a. Write the differential equation for v(t). b. Find the damping coefficient, the natural frequency, and the form of the complementary solution. c. Usually, for a sinusoidal forcing function, we try a particular solution of the form v p ( t)=A cos( 10 4 t )+B sin( 10 4 t ). Why doesn’t that work in this case? d. Find the particular solution. [Hint: Try a particular solution of the form v p ( t)=At cos( 10 4 t )+B t sin( 10 4 t ). ] e. Find the complete solution for v(t).
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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Similar questions
- 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.arrow_forwardH4.arrow_forwardUse the defining law for a capacitor to find the current iC(t) corresponding to the voltage shown in Figure P4.27. Sketch your result.arrow_forward
- Write the differential equation for i L(t) and find the complete solution for the circuit of Figure P4.45. [Hint: Try a particular solution of the form i Lp ( t )=A e −t .]arrow_forwardThe circuit shown in Figure P4.24 has been set up for a long time prior to t=0 with the switch closed. Find the value of vC prior to t=0. Find the steady-state value of vC after the switch has been opened for a long time.arrow_forward4.5 Write the differential equation for t> 0 for vc in Figure P4.32. t=0 ow R₂ DIO R₁ Figure P4.32 + CVCarrow_forward
- We know that the capacitor shown in Figure P4.11 is charged to a voltage of 10 V priorto t=0.a. Find expressions for the voltage across the capacitor vC(t) and the voltage across theresistor vR(t) for all time.b. Find an expression for the power delivered to the resistor.c. Integrate the power from t=0 to t=∞ to find the energy delivered.d. Show that the energy delivered to the resistor is equal to the energy stored in thecapacitor prior to t=0.arrow_forwardThe current waveform shown in Figure P4.23 flowsthrough a 2-H inductor. Plot the inductor voltage vL(t).arrow_forwardFind the energy stored in each capacitor andinductor, under steady-state conditions, in the circuitshown in Figure P4.11.arrow_forward
- For the circuit shown in the Figure P4.65, find thefrequency that causes the equivalent impedance toappear purely resistive.arrow_forwardTitle Find the capacitor voltage in the network shown in Figure P4.2 if the switch closes at t = 0. Assume Description Find the capacitor voltage in the network shown in Figure P4.2 if the switch closes at t = 0. Assume zero initial conditions. Also find the time constant, rise time, and settling time for the capacitor voltage. /=0) W 1.802 0.79 F FIGURE P4.2 Plot the step response for Problem 4 using MATLAB. From your plots, find the time constant, rise time, and settling timearrow_forwardIf the plots shown in Figure P4.19 are the voltageacross and the current through an ideal inductor,determine the inductance.arrow_forward
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