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/sec = 377 rad/sec Peak I max = 10 Amps RMS I rms = 10/ 2 = 7.071 Amps iii. Instantaneous currents in the two circuit elements when the instantaneous voltage is 10 volts.

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When v(t) = 10 sin wt = 10 Or sin wt = 1 = sin 90 0 Therefore, wt = 90 0 At wt = 90 0 : i 1 = 10 sin 90 0 = 10 Amps and i 2 = 10 sin (90 0 +90 0 ) = 0 Amps Alternate Solution: From the Figure, When v (t) = 10 volts, Element 1 : i 1 (t) = 10 Amps Element 2 : i 2 (t) = 0 Amps 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 Therefore, (I 1 +I 2 ) = 14.1 /45 0 Amps peak (i1 + i2) = 14.1 sin (wt + 45 0 ) Amps Check: 10 cm (10 V) 10 cm (10 V) 14.1 cm (14.1 V) 45 0
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This note was uploaded on 09/25/2010 for the course EE 212 taught by Professor Gander during the Spring '10 term at University of Saskatchewan- Management Area.

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

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