1. Problems and Solutions 不要用看的，要動手！
CHAPTER 4
Problems and Solutions
不要用看的，要動手！

2. Problem 4 ω = 2,000 rad/s = 2π/T T = 2 π ÷ 2000 rad/s = 3.142 ms
How long will it take the following waveform to pass through 10 cycles?
ω = 2,000 rad/s = 2π/T
T = 2 π ÷ 2000 rad/s = ms
走10個cycles 需要 10× T = ms

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

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

5. Problem 7 電流領先電壓 56° 電流領先電壓140°
What is the phase relationship between the following pairs of waveforms?
相角-72°
相角-16°
電流領先電壓 56°
電流領先電壓140°

6. i的 peak value 為6 μA ，且領先電壓40°  i (t) = 6×10-6A sin(1000t+46°)
Problem 8
Write the sinusoidal expression for a current i that has a peak value of 6 μA and leads the following voltage by 40°
i的 peak value 為6 μA ，且領先電壓40°
 i (t) = 6×10-6A sin(1000t+46°)

7. v的 peak value 為48 mV ，且落後電流60°  v (t) = 48×10-3V sin(ωt-90°)
Problem 9
Write the sinusoidal expression for a voltage V that has a peak value of 48 mV and lags the following current I by 60°
v的 peak value 為48 mV ，且落後電流60°
 v (t) = 48×10-3V sin(ωt-90°)

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

9. Problem 11
Write 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°

10. Problem 12
Determine the average value of the following.

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

12. Problem 14 Determine the average value of the waveform in Fig. 4.81.
求出交點

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

14. Problem 16
Determine the sinusoidal expression for the voltage drop across a 1.2-kΩ resistor if the current iR is 8×10-3 sin 200t.
Find the power delivered to the resistor.
What is the power factor of the load?

15. Problem 17
Find the sinusoidal expression for the current through a 2.2-kΩ 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.

16. Problem 18
Find 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?
電壓領先電流90º

17. Problem 19 Determine the sinusoidal expression for the current ic of a
10-μF capacitor if the vo1tage across the capacitor is Vc =
20× 10-3 sin(2000t + 30°)
電流領先電壓90º

18. Problem 20
For 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(200t－10° )
2. v = 0.12 sin(1000t + 10° )
i = 6×10-3cos(1000t + 10° )

19. v = 16 sin(200t + 80° ) i = 0.04 sin(200t－10° )
電流落後電壓90º，為電感。

20. v = 0.12 sin(1000t + 10°)
i = 6×10-3cos(1000t + 10° ) = 6×10-3sin(1000t+100°)
電流領先電壓90º，為電容。

21. Problem 21
For 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° )

22. Problem 22
Convert the following to the other domain.

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

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

25. 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°).

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

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

28. 再度提醒

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

30. 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 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.
h. The phasor diagram. i. The Fp of the network.
j. The current and voltages in the time domain.

31. The reactance of the capacitor.
b. The total impedance and the impedance diagram.
c. The current I

32. 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

33. leading 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

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

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

36. 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.

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

38. Problem 34 For the parallel RC network in Fig. 4.89, determine:
a. The admittance diagram
b. YT, ZT
c. 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

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

40. Problem 36
Find the currents I1 and I2 in Fig using the current divider
rule. If necessary, review Section 2.10.

41. Problem 37 For the parallel RLC network in Fig. 4.92, determine:
a. The admittance diagram.
b. YT, ZT
c. 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.

43. lagging

44. 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.

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