Test 1 Solutions - Fall 2003
Problem 4

The Thevenin equivalent resistance of the circuit below is 5 KW. Determine R.

First, note that the equivalent resistance of the dependent source in parallel with the unknown resistor R MUST be 2K, since that euivalent resistance is in series with the 3K, and the sum is known to be 5K. Thus we can solve the slightly simpler problem of what is R so that the dependent source in parallel with R is 2K.

I will connect a test source of 1 V to the circuit. Since the equivalent resistance is 2K, the current delivered to the circuit from the source must be 500 mA. (I = 1 / 2K)

Since everything is in parallel, VR = 1 V. Therefore, the current through the dependent source is 0.0001 amperes or 100 mA. KCL immediately implies that the current through the resistor R must be 400 mA. Now Ohm's Law gives

R = 1 V / 400 mA
R = 2.5 KW

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Test 1, Fall 2003
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