9.53 The circuit shown in Fig. P9.53 is operating at a fre- quency of 10 rad/s. Assume a is real and lies between -10 and +10, that is, – 10 < a < 10. a) Find the value of a so that the Thévenin imped- ance looking into the terminals a,b is purely resistive. b) What is the value of the Thévenin impedance for the a found in (a)? c) Can a be adjusted so that the Thévenin impedance equals 500 – j500 N? If so, what is the value of a? d) For what values of a will the Thévenin imped- ance be inductive? Figure P9.53 100 µF HE a avA be

9.53 The circuit shown in Fig. P9.53 is operating at a fre- quency of 10 rad/s. Assume a is real and lies between -10 and +10, that is, – 10 < a < 10. a) Find the value of a so that the Thévenin imped- ance looking into the terminals a,b is purely resistive. b) What is the value of the Thévenin impedance for the a found in (a)? c) Can a be adjusted so that the Thévenin impedance equals 500 – j500 N? If so, what is the value of a? d) For what values of a will the Thévenin imped- ance be inductive? Figure P9.53 100 µF HE a avA be

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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The frequency of the source voltage in the circuit isadjusted until vg is in phase with ig. What is the value of ω inradians per second?2. If ig=60 cosωt mA (where ω is the frequency found in [a]), what isthe steady-state expression for vg?
a) Calculate the range of values K will take for the steady-state error to be “??? ≤ 0.04” when the input of the system is ?(?) = ?. b) Calculate the value range that K will take so that the damping ratio can be “1 > ξ ≥ 1 2√6”. c) Calculate the damping ratio “ξ” and the undamped natural frequency ?? value so that “? = 0.5”.
A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency v. Let the source voltage be given by v = Vcosvt. (a) Show that each of the instantaneous voltages vR, vL, and vC at any instant is equal to v and that i = iR + iL + iC, where i is the current through the source and iR, iL, and iC are the currents through the resistor, inductor, and capacitor, respectively. (b) What are the phases of iR, iL, and iC with respect to v? Use current phasors to represent i, iR, iL, and iC. In a phasor diagram, show the phases of these four currents with respect to v. (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is I = √(I2R) + (IC - IL)2 . (d) Show that the result of part (c) can be written as I = V/Z, with 1/Z = √ (1/R2) + [ωC - (1/ωL)]2.
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At t=−2 ms, a sinusoidal voltage is known to be zero and goingpositive. The voltage is next zero at t=8 ms. It is also known that thevoltage is 80.9 V at t=0.1. What is the frequency of v in hertz?2. What is the expression for v?
You are studying a solenoid of unknown resistance and inductance. You connect it in series with a 50.0 Ω resistor, a 25.0 V battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digitally record the voltage vR across the resistor as a function of the time t that has elapsed after the switch is closed. Your measured values are shown in Fig. P30.68, where vR is plotted versus t. In addition, you measure that vR = 0 just after the switch is closed and vR = 25.0 V a long time after it is closed. (a) What is the resistance RL of the solenoid? (b) Apply the loop rule to the circuit and obtain an equation for vR as a function of t. (c) According to the equation that you derived in part (b), what is vR when t = t, one time constant? Use FIG to estimate the value of t = t. What is the inductance of the solenoid? (d) How much energy is stored in the inductor a long time after the switch is closed?
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