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In the given circuit, r is a variable resistor. The heat dissipated in r is maximum when r = f*R. Determine the value of f.

1. 1
2. 1/4
3. 1/2
4. 3/4

Correct answer: 1/2

Solution

Heat generated in r is P = I² * r. Maximum power transfer to a variable load occurs when the load equals the equivalent resistance of the source network seen from the load terminals. For this circuit the Thevenin resistance across r equals R/2, so r must equal R/2, giving f = 1/2.

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