# soln1 - EE 212 Assignment 1 Solutions Problem 1 i Voltage...

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EE 212 – Assignment 1 Solutions Problem # 1 i. Voltage and Current Waveforms for the two circuit elements ii. Time period, angular frequency, peak and RMS values of the current i 2 (t) Time period f = 60 Hz T = 1/f = 1/60 = 0.01667 seconds Angular Frequency ϖ = 2 ×π× f = 2 ×π× 60 = 120 π rad/s = 377 rad/s Peak I max = 10 A RMS I rms = 10/ 2 = 7.07 A

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iii. Instantaneous currents in the two circuit elements when the instantaneous voltage is 10 volts. When v(t) = 10 sin ωt = 10 Or sin ωt = 1 = sin 90 0 Therefore, ωt = 90 0 At ωt = 90 0 : i 1 = 10 sin 90 0 = 10 A and i 2 = 10 sin (90 0 +90 0 ) = 0 A Alternate Solution: From the Figure, When v (t) = 10 volts, Element 1 : i 1 (t) = 10 A Element 2 : i 2 (t) = 0 A iv. Total current i(t) drawn from the source. From Phasor Diagram: I 1 = 10 cm for 10 V I 2 = 10 cm for 10 V (I 1 +I 2 ) = diagonal = 14.1 cm i.e. 14.1 V, at an angle = 45 0 10 cm (10 V) 10 cm (10 V) 14.1 cm (14.1 V) 45 0
Therefore, (I 1 +I 2 ) = 14.1 /45 0 A peak (i1 + i2) = 14.1 sin (ωt + 45

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soln1 - EE 212 Assignment 1 Solutions Problem 1 i Voltage...

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