CHAPTER 4Problems and Solutions

Problem 4How long will it take the following waveform to pass through 10 cycles? = 2,000 rad/s = 2/TT = 2 2000 rad/s = 3.142 ms10cycles 10 T = 31.42 ms

Problem 5At what instant of time will the following waveform be 6 V? Associate t = 0s with of sin equal to 0.

Problem 6 At what angle (closest to 0) will the following waveform reach 3 mA? i = 8.6 10-3 sin 500t At what time t will it occur?

Problem 7What is the phase relationship between the following pairs of waveforms? 56140-72-16

Problem 8Write the sinusoidal expression for a current i that has a peak value of 6 A and leads the following voltage by 40i peak value 6 A 40

i (t) = 610-6A sin(1000t+46)

Problem 9Write the sinusoidal expression for a voltage V that has a peak value of 48 mV and lags the following current I by 60v peak value 48 mV 60

v (t) = 4810-3V sin(t-90)

Problem 10Determine the effective value of each of the following.

Problem 11Write the sinusoidal expression for each quantity using the information provided Ieff = 36 mA, f = 1 kHz, phase angle = 60 Veff = 8V, f =60 Hz, phase angle = -10

Problem 12Determine the average value of the following.

Problem 13Determine the average value of the waveform in Fig. 4.80.

Problem 14Determine the average value of the waveform in Fig. 4.81.

Problem 15Determine the average value of i2 from = 0 to if i = 6 sin (integral calculus required).

Problem 16Determine the sinusoidal expression for the voltage drop across a 1.2-k resistor if the current iR is 810-3 sin 200t.Find the power delivered to the resistor.What is the power factor of the load?

Problem 17Find the sinusoidal expression for the current through a 2.2-k resistor if the power delivered to the resistor is 3.6 W at a frequency of 1000 Hz.Find the sinusoidal expression for the voltage across the resistor.

Problem 18Find the sinusoidal expression for the voltage drop across a 20-mH coil if the current iL is 4 sin(500t + 60)Find the power delivered to the coil. What is the power factor of the load?90

Problem 19Determine the sinusoidal expression for the current ic of a10-F capacitor if the vo1tage across the capacitor is Vc =20 10-3 sin(2000t + 30)90

Problem 20For the following pairs determine whether the element is a resistor, inductor, or capacitor.Determine the resistance, inductance, or capacitance.1. v = 16 sin(200t + 80 ) i = 0.04 sin(200t10 )2. v = 0.12 sin(1000t + 10 ) i = 610-3cos(1000t + 10 )

v = 16 sin(200t + 80 ) i = 0.04 sin(200t10 )90

v = 0.12 sin(1000t + 10)

i = 610-3cos(1000t + 10 ) = 610-3sin(1000t+100) 90

Problem 21For the following pairs determine the power delivered to the load.Find the power factor and indicate whether it is inductive or capacitive.1. v = 1600 sin(377t + 360 ) i = 0.8 sin(377t + 60 )2. v = 100 sin(106t 10 ) i = 0.2 sin(106t 40 )

Problem 22Convert the following to the other domain.

Problem 23Perform the following operations. State your answer in polar form.

Problem 24 Using phasor notation, determine the vo1tage (in the time domain) across a 2.2-k resistor if the current through the resistor is i = 20 10-3 sin (400t + 30).

Problem 25 Using phasor notation, determine the current (in the time domain) through a 20-mH coil if the voltage across the coil is vL = 4 sin(1000t + 10).

Problem 26 Using phasor notation, determine the voltage (in the time domain) across a 10-F capacitor if the current ic = 4010-3 sin(10t + 40).

Problem 27 For the system in Fig. 4.82, determine the vo1tage v1 in the time domain.

Problem 28 For the system in Fig. 4.83, determine the current i in the time domain.

Problem 29 For the series ac network in Fig. 4.84, determine:a. The reactance of the capacitor.b. The total impedance and the impedance diagram.c. The current Id. The voltages VR and VC using Ohm's law.e. The voltages VR and VC using the voltage-divider rule.f. The power to Rg. The power supplied by the voltage source e.h. The phasor diagram. i. The Fp of the network.j. The current and voltages in the time domain.

The reactance of the capacitor.

b. The total impedance and the impedance diagram.

c. The current I

d. The voltages VR and VC using Ohm's law.e. The voltages VR and VC using the voltage-divider rule.

f. The power to R

g. The power supplied by the voltage source e.

i. The Fp of the network.

j.The current and voltages in the time domain.leading

Problem 30 Repeat Problem 29 for the network in Fig. 4.85 , after making the appropriate changes in parts (a), (d) and (e).

Problem 31 Determine the voltage vL (in the time domain) for the network in Fig. 4.86 using the voltage-divider rule.

Problem 32 For the series RLC network in Fig. 4.87, determine:a. ZT b. I. c. VR, VL, VC using Ohm's law.d. VL using the voltage-divider rule.e. The power to R. f. The Fp.g. The phasor and impedance diagrams.

Problem 33 Determine the voltage VC for the network in Fig. 4.88 using the voltage-divider rule.

Problem 34 For the parallel RC network in Fig. 4.89, determine:a. The admittance diagramb. YT, ZTc. I.d. IR, IC using Ohm's law.e. The total power delivered to the network.f. The power factor of the network.g. The admittance diagram

Problem 35 Repeat Prob1em 34 for the network in Fig. 4.90, replacing IC with IL in part (d).

Problem 36Find the currents I1 and I2 in Fig. 4.91 using the current dividerrule. If necessary, review Section 2.10.

Problem 37 For the parallel RLC network in Fig. 4.92, determine:a. The admittance diagram.b. YT, ZTc. I, IR, IL, and IC.d. The total delivered power.e. The power factor of the network.f. The sinusoidal format of I, IR, IL, and IC.g. The phase relationship between e and iL.

lagging

Problem 38 For the network in Fig. 4.93, determine:a. The short-circuit currents I1 and I2 ,b. The voltages V1 and V2 .c. The source current I.

Problem 39Determine the current I and the voltage V for the network in Fig. 4.94