Tutorial circuits for engineering, Exercises of Circuit Theory

Download Tutorial circuits for engineering and more Exercises Circuit Theory in PDF only on Docsity! 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: 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 , For T2 = 30 ms , f2 = 1/ 30 x10 -3 = 33.3 Hz. 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)