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Phasor Analysis Solution

# Phasor Analysis Solution - EE 2011 Practice Problems Phasor...

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EE 2011 Practice Problems Phasor Analysis Solution Q1 The circuit shown is driven by v g = V g cos( ϖ t). a) Find the phasor current I R in the circuit shown. Express your answer in polar phasor form. b) Find i R (t). + v g _ L C R I R Answer: a) I R = (V g 0 o * (1/jwC)||R / [jwL+(1/jwC)||R]) / R = [V g / sqrt((R-w 2 LCR) 2 +w 2 L 2 )] arctan(wL/( w 2 LCR-R)) b) i R (t) = [V g / sqrt((R-w 2 LCR) 2 +w 2 L 2 )] cos(wt + arctan(wL/(w 2 LCR-R))) Actually you can have more accurate answers in terms of w value. Such as what if w 2 LCR-R=0.

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Q2 The circuit shown is driven by v g (t) = V g cos( ϖ t). 1. Calculate the current passing through the resistance 2R on the right hand side in terms of Vg, R, L, and C. Express your answer in polar phasor form. 2. Write down the expression for this current in time varying form. C Vg R L 2R Answer: a) I 2R = (V g 0 o * (1/jwC)||2R / [jwL+R+(1/jwC)||2R]) / 2R = [V g / sqrt((3R-2w 2 LCR) 2 +(2wCR 2 +wL) 2 ] arctan((2wCR 2 +wL)/(2w 2 LCR-3R)) b) I 2R (t) = [V g / sqrt((3R-2w 2 LCR) 2 +(2wCR 2 +wL) 2 ] cos(wt + arctan((2wCR 2 +wL)/(2w 2 LCR-3R))) Actually you can have more accurate answers in terms of w value. Such as what if 2w 2 LCR – 3R=0.
Q3 Use phasor techniques to find v O (t). 10 mhy 100 μ fd 10 120 cos(1000t) V rms + v O (t) - Answer: V o = 120 0 o * (jwL)||R / [1/jwC+(jwL)||R] = 120 0 o * 1 90 o v o (t) = 120cos(1000t+90 o )

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Q4
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