Analysis
1. Determine the AC peak and RMS voltages, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 10 \sin 2\pi 1000 t\)
2. Determine the AC peak and RMS voltages, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 0.4 \sin 2\pi 5000 t\)
3. Determine the peak AC portion voltage, DC offset, frequency, period and phase shift for the following expression: \(v(t) = −3 + 20 \sin 2\pi 50 t\)
4. Determine the peak AC portion voltage, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 12 + 2 \sin 2\pi 20000 t\)
5. Determine the AC peak and RMS voltages, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 10 \sin (2\pi 100 t + 45^{\circ} )\)
6. Determine the AC peak and RMS voltages, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 5 \sin (2\pi 1000 t − 90^{\circ} )\)
7. Determine the peak AC portion voltage, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 10 + 1 \sin (2\pi 400 t − 45^{\circ} )\)
8. Determine the peak AC portion voltage, DC offset, frequency, period and phase shift for the following expression: \(v(t) = 10 + 10 \sin (2\pi 5000 t + 30^{\circ} )\)
9. A 1 kHz sine wave has a phase of 72\(^{\circ}\). Determine the time delay. Repeat for a 20 kHz sine wave.
10. A 2 kHz sine wave has a phase of 18\(^{\circ}\). Determine the time delay. Repeat for a 100 kHz sine wave.
11. An oscilloscope measures a time delay of 0.2 milliseconds between a pair of 500 Hz sine waves. Determine the phase shift.
12. An oscilloscope measures a time delay of −10 microseconds between a pair of 20 kHz sine waves. Determine the phase shift.
13. Convert the following from rectangular to polar form:
a) \(10 + j10\)
b) \(5 − j10\)
c) \(−100 + j20\)
d) \(3k + j4k\)
14. Convert the following from rectangular to polar form:
a) \(2k + j1.5k\)
b) \(8 − j8\)
c) \(−300 + j300\)
d) \(−1k − j1k\)
15. Convert these from polar to rectangular form:
a) \(10\angle 45^{\circ} \)
b) \( 0.4\angle 90^{\circ} \)
c) \(−9\angle 60^{\circ} \)
d) \(100\angle −45^{\circ} \)
16. Convert these from polar to rectangular form:
a) \(−4\angle 60^{\circ} \)
b) \(−0.9\angle 30^{\circ} \)
c) \(5\angle 120^{\circ} \)
d) \(6\angle −135^{\circ} \)
17. Perform the following computations:
a) \((10 + j10) + (5 + j20)\)
b) \((5 + j2) + (−5 + j2)\)
c) \((80 − j2) − (100 + j2)\)
d) \((−65 + j50) − (5 − j200)\)
18. Perform the following computations:
a) \((100 + j200) + (75 + j210)\)
b) \((−35 + j25) + (15 + j8)\)
c) \((500 − j70) − (200 + j30)\)
d) \((−105 + j540) − (5− j200)\)
19. Perform the following computations:
a) \((100 + j200) \cdot (75 + j210)\)
b) \((−35 + j25) \cdot (15 + j8)\)
c) \((500 − j70) / (200 + j30)\)
d) \((−105 + j540) / (5− j200)\)
20. Perform the following computations:
a) \((10 + j10) \cdot (5 + j20)\)
b) \((5 + j2) \cdot (−5 + j2)\)
c) \((80 − j2) / (100 + j2)\)
d) \((−65 + j50) / (5− j200)\)
21. Perform the following computations:
a) \((10\angle 0^{\circ} ) \cdot (10\angle 0^{\circ} )\)
b) \((5\angle 45^{\circ} ) \cdot (−2\angle 20^{\circ} )\)
c) \((20\angle 135^{\circ} ) / (40\angle −10^{\circ} )\)
d) \((8\angle 0^{\circ} ) / (32\angle 45^{\circ} )\)
22. Perform the following computations:
a) \((0.3\angle 0^{\circ} ) \cdot (3\angle 180^{\circ} )\)
b) \((5\angle −45^{\circ} ) \cdot (−4\angle 20^{\circ} )\)
c) \((0.05\angle 95^{\circ} ) / (0.04\angle −20^{\circ} )\)
d) \((500\angle 0^{\circ} ) / (60\angle 225^{\circ} )\)
23. Perform the following computations:
a) \((0.3\angle 0^{\circ} ) + (3\angle 180^{\circ} )\)
b) \((5\angle −45^{\circ} ) + (−4\angle 20^{\circ} )\)
c) \((0.05\angle 95^{\circ} ) − (0.04\angle −20^{\circ} )\)
d) \((500\angle 0^{\circ} ) − (60\angle 225^{\circ} )\)
24. Perform the following computations:
a) \((10\angle 0^{\circ} ) + (10\angle 0^{\circ} )\)
b) \((5\angle 45^{\circ} ) + (−2\angle 20^{\circ} )\)
c) \((20\angle 135^{\circ} ) − (40\angle −10^{\circ} )\)
d) \((8\angle 0^{\circ} ) − (32\angle 45^{\circ} ) \)
25. Determine the capacitive reactance of a 1 \(\mu\)F capacitor at the following frequencies:
a) 10 Hz
b) 500 Hz
c) 10 kHz
d) 400 kHz
e) 10 MHz
26. Determine the capacitive reactance of a 220 pF capacitor at the following frequencies:
a) 10 Hz
b) 500 Hz
c) 10 kHz
d) 400 kHz
e) 10 MHz
27. Determine the capacitive reactance at 50 Hz for the following capacitors:
a) 10 pF
b) 470 pF
c) 22 nF
d) 33 \(\mu\)F
28. Determine the capacitive reactance at 1 MHz for the following capacitors:
a) 22 pF
b) 560 pF
c) 33 nF
d) 4.7 \(\mu\)F
29. Determine the inductive reactance of a 100 mH inductor at the following frequencies:
a) 10 Hz
b) 500 Hz
c) 10 kHz
d) 400 kHz
e) 10 MHz
30. Determine the inductive reactance of a 100 mH inductor at the following frequencies:
a) 10 Hz
b) 500 Hz
c) 10 kHz
d) 400 kHz
e) 10 MHz
31. Determine the inductive reactance at 1 kHz for the following inductors:
a) 10 mH
b) 500 mH
c) 10 \(\mu\)H
d) 400 \(\mu\)H
32. Determine the inductive reactance at 500 kHz for the following inductors:
a) 1 mH
b) 40 mH
c) 2 \(\mu\)H
d) 50 \(\mu\)H
33. Draw phasor diagrams for the following:
a) \(5 + j2\)
b) \(−10 −j20\)
c) \(8\angle 45^{\circ} \)
d) \(2\angle −35^{\circ} \)
34. Draw phasor diagrams for the following:
a) \(60j−20\)
b) \(−40 + j500\)
c) \(0.05\angle −45^{\circ} \)
d) \(−15\angle 60^{\circ} \)
35. The fundamental of a certain square wave is a 5 volt peak, 1 kHz sine. Determine the amplitude and frequency of each of the next five harmonics.
36. The fundamental of a certain triangle wave is a 10 volt peak, 100 Hz sine. Determine the amplitude and frequency of each of the next five harmonics.