Quiz1soln2 - MAE140 Linear Circuits Quiz 1 Solutions...

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MAE140 Linear Circuits Quiz # 1 --- October 17, 2002 Solutions Question 1 --- Circuit Concepts (a) Begin by computing the current and voltage of the load resistors. R 1 = 40 W : P = 40 W , i = 1 A , v = 40 V R 1 = 10 W : P = 40 W , i = 2 A , v = 20 V Now use the circuit properties. Do this first with the Norton-type circuit on the left. i eq = ( G 1 + G eq ) v = ( 1 40 + G eq )40 = 40 G eq + 1, case R 1 = 40 W i eq = ( 1 10 + G eq ) v = ( 1 10 + G eq )20 = 20 G eq + 2, case R 1 = 10 W Subtract second equation from first: G eq = 1 20 S , R eq = 20 W Solve for i eq = 3 A . Using the Thévenin variant on the right yields a different set of equations. 40 = 40 R eq + 40 v eq or 40 R eq + 1600 = 40 v eq or R eq + 40 = v eq , case R 1 = 40 W 20 = 10 R eq + 10 v eq or 20 R eq + 200 = 10 v eq or 2 R eq + 20 = v eq , case R 1 = 10 W Subtract first equation from second: R eq = 20 W . Then solve for v eq = 60 V . Of course one solution is transformable into the other using a source transformation. (b) 1. Transform the left (20V-100 W ) pair into their Norton (200mA-100 W ) equivalent. Now rearrange the parallel elements.
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