Circuit 2
Tutorial 1 problem solutions
Dr. Mohammed Tawfeeq
Problem 1. An alternating voltage is given by v = 282.8 sin 314t volts. Find (a) the rms
voltage, (b) the frequency and (c) the instantaneous value of voltage when t = 4 ms.
Problem 2. An alternating voltage is given by
v = 75 sin (200πt - 0.25)
volts.
Find (a) the amplitude, (b) the peak-to-peak value, (c) the rms value, (d) the periodic time, (e)
the frequency, and (f) the phase angle (in degrees and minutes) relative to 75 sin 200πt
Solution
Problem 3. An alternating voltage, v, has a periodic time of 0.01 s and a peak value of 40 V.
When time t is zero, v = -20 V.
Express the instantaneous voltage in the form
.
Solution:
Problem 4. The current in an a.c. circuit at any time t seconds is given by: i = 120 sin(100πt +
0.36 ) amperes. Find:
(a) the peak value, the periodic time, the frequency and phase angle relative to 120 sin 100πt
(b) the value of the current when t = 0
(c) the value of the current when t = 8 ms
(d) the time when the current first reaches 60 A, and
(e) the time when the current is first a maximum
Problem 5. For the waveform in Figure 1, determine the frequency.
FIGURE 1
Solution :
From the figure T= 4 ms, hence f = 1/T = 1/4x10-3 = 250 Hz .
Problem 6 . Two waveforms have periods of T1 = 10 ms and T2 =30 ms respectively. Which
has the higher frequency? Compute the frequencies of both waveforms.
Solution:
For T1 = 10 ms , f1 = 1/ 10 x 10-3= 100 Hz ,
Hz.
For T2 = 30 ms
, f2 = 1/ 30 x10-3= 33.3
Hence f1 is higher.
Problem7 . Two sources have frequencies f1 and f2 respectively. If f2 = 20f1, and T2 is 1 ms,
what is f1? What is f2?
Problem 8. Consider Figure 2. What is the frequency of the waveform?
FIGURE 2
SOLUTION:
100 ms for 2.25 cycles.
Time of one cycle = 100 ms / 2.25 = 44.44 ms. Hnce f = 1/T = 1/44.44 =22.5 Hz.
Problem 9 . If the amplitude of the waveform of Figure 3 is Em =100 V, determine the coil
voltage at 30° and 330°.
FIGURE 3
Ans: 50 V
, -50 V
Problem10. If the coil of Figure 4 rotates at ω = 300°/s, how
long does it take to complete one revolution?
Ans: 1.2 second
Fig.4
Problem 11 . If the coil of Figure 4 rotates at 3600 rpm, determine its angular velocity, ω in
degrees per second.
Ans:
21 600 deg/s
Problem 12 . If ω= 240 rad/s, what are T and f ? How many cycles occur in 27 s ?
Ans : 26.18 ms, 38.2 Hz, 1031 cycles
Problem 13 . If 56 000 cycles occur in 3.5 s, what is ω?
Problem 14 . Given v =20 sin(ωt + 30°) and i = 18 sin(ωt + 40°), determine phase
relationships, and sketch the waveforms.
Solution:
Ans: 70°
Problem
15
(a)