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ee341_h01_Wi2012

ee341_h01_Wi2012 - t v c c jX 1 R 2 R 1 jX 1 Derive the...

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ECE 341 Homework #1 Winter 2012 Due: Wed. 18 Jan., in class (Total: 20 points) Problem 1: Instantaneous ac power is defined as ) cos( 2 ) cos( 2 ) ( ) ( ) ( I RMS V RMS t I t V t i t v t p , 1. Use simple trigonometric identities to demonstrate that ) 2 cos( ) (cos( 2 ) ( ) ( ) ( I V I V RMS RMS t I V t i t v t p (2 pts.) 2. Average power of an ac circuit is defined as t T t dt t p T P ) ( 1 , where and T is the period of p(t) . Derive the equation that ) cos( I V RMS RMS I V P . (3 pts.) Note : T is the inverse of the frequency. The period of p(t) is defined by the ac component, which has an angular speed of 2 . Problem 2: RMS of a voltage is defined as t T t RMS dt t v T V 2 )] ( [ 1 , where ) cos( ) ( V p t V t v and T is the period of ) ( t v . Based on the above equation, derive the equation 2 / p RMS V V . (2 pts.) Problem 3 : In the following circuit, t t v a cos 120 2 ) ( , 1 2 1 1 L X R R X ohm, 1 C X ohm where loss r is the cable resistance between the power supply and load.

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Unformatted text preview: +-) ( t v c c jX 1 R 2 R 1 jX 1) Derive the phasors for the following signals: I ~ l V ~ c V ~ ; (3 pts.) 2) Draw a phasor diagram that shows a V ~ I ~ l V ~ c V ~ ; (2 pts.) 3) Calculate the reactive power consumed by X L and X c ; (2 pts.) 4) Calculate the power factor of the circuit. (3 pts.) Problem 4 :Graph the following time varying quantities v(t) i(t) the product v(t) i(t) where v(t) = 2 2 sin( t) i(t) = 1 2 sin( t + π ) Assume a frequency of 60 Hz. The time axis for the graphs should be from 0 to 2T (where T is the period of the waveforms) All waveforms should be on the same graph ; identify each waveform, label axis and scale. Any plotting software can be used, Matlab, MathCad, even Excel (or other spread sheet software). (3 pts.)...
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