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 4.3P
The initial voltage across the capacitor shown in Figure P4.3 is
Figure P4.3
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Suppose we have a capacitance C discharging through a resistance R. Define and give an expression for the time constant. To attain a long time constant, do we need large or small values for R? For C?
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 βleakageβ 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 ΞΌF, RC = 100 MΞ©, R1 = R2 = 1 ΞΌΞ© andL1 = L2 = 0.1 ΞΌH, find the equivalent impedanceseen at the terminals a and b as a function offrequency Ο.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.
The voltage across an inductor plotted as a functionof time is shown in Figure P4.14. If L = 0.75 mH,determine the current through the inductor att = 15 ΞΌs.
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
- Use 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_forwardIn the first method to write the equation, why is the capacitor value not included in the equation at first?arrow_forwardWhen we talk about capacitance of capacitor we normally say that capacitance depends on the size, shape, and position of the two capacitors and dielectric constant K. What then did we mean when we say that capacitance is constant in the equation Q = CV?arrow_forward
- 1. Inquire about the operational and geometric definitions of capacitance C. [C = = Ξ΅0 , please refer to previous lesson on capacitance.] 2. Have the students write down the meaning of each of the symbols present in the above definitions.arrow_forwardDetermine expressions for and sketch v R ( t ) to scale versus time for the circuit of Figure P4.43. The circuit is operating in steady state with the switch closed prior to t=0. Consider the time interval β1β€tβ€5 ms.arrow_forwardThe initial voltage across the capacitor shown in Figure P4.3 is v C ( 0+ )=β10 V. Find anexpression for the voltage across the capacitor as a function of time. Also, determine the time t0at which the voltage crosses zero.arrow_forward
- What current flows through an ideal capacitor if the voltage across the capacitor is constant with time? To what circuit element is an ideal capacitor equivalent in circuits for which the currents and voltages are constant with time?arrow_forwardThe 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 tβ₯0. Sketch iL(t) to scale versus timearrow_forwardThe figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ξ©). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoffβs Law givesarrow_forward
- What are the minimum and maximum values of capacitance that can be obtained by connecting four 2-ΞΌF capacitors in series and/or parallel? How should the capacitors be connected?arrow_forwardWe 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=β 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_forwardWhat is the equation thst represents the relationship between charge, capacitance and voltage for a capacitor.arrow_forward
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