REVIEW-Phasors

# REVIEW-Phasors - THINGS YOU SHOULD KNOW ABOUT PHASORS...

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Unformatted text preview: THINGS YOU SHOULD KNOW ABOUT PHASORS (Lectures 29-36) 1. How to transform a circuit to the phasor domain, i.e., convert sources and computer impedances. 2. How to analyze basic circuits using KCL and KVL 3. How to use Node-Voltage and Mesh-Current Methods 4. How to compute the Thevenin equivalent of a complex circuit. PAGE TRANSFORMATIONS AND SIMPLE CALCULATIONS 2 PHASE-SHIFT CALCULATIONS 3-4 KCL &amp; KVL 5-9 NODE VOLTAGE &amp; MESH CURRENT 10-12 THEVENIN &amp; NORTON EQUIVALENT 13-15 ENGR 210 REVIEWS Phasors Page 1 ENGR 210 REVIEWS Phasors Page 2 ENGR210 HW11 Solutions Page 4 Problem 4 Adjust Source Frequency to Achieve Zero Phase (a) The frequency of the source voltage in the circuit shown above is adjusted until i g is in phase with v g . What is the value of in radians per second? SOLUTION As is usually with problems of this type we convert the problem to phasors. The equivalent impedance see by the voltage source is Z eq = 500 + 1 j C + 1000 j L = 500 + 1 j (10 6 ) + 1000( j 0.5) 1000 + j 0.5 Z eq =500- 10 6 j+ 1000 2 +2 10 6 j 2000 2 + 2 For i g to be in phase with v g the imaginary components of Z eq need to sum to zero which requires that 10 6 + 2 10 6 2000 2 + 2 = 0 . Simple algebra gives = 2000 rad / s for this to be true. (b) If v g = 20cos t V (where is the frequency found in [a]), what is the steady-state expression for v o ? SOLUTION We can use the real part of the result from (a) and evaluate it for = 2000 to get ENGR 210 REVIEWS Phasors Page 3 ENGR210 HW11 Solutions Page 5 Z eq = 500- 10 6 2000 j+ 1000(2000 2 )+2 10 6 j 2000 2000 2 + 2000 2 =500-500j+500+500j=1000 Using Ohms Law we can evaluate the current as i g = 20 1000...
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## REVIEW-Phasors - THINGS YOU SHOULD KNOW ABOUT PHASORS...

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