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GATE 2020 EE – Question 42

Electric Circuits · Network Theorems: Thevenin, Norton, Superposition and Maximum Power Transfer theorem · 2 marks · Multiple choice

A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0 A. When connected to an ideal rheostat, find the load resistance value at which maximum power is transferred, and the corresponding load voltage and current.

  1. Short, $\infty$ A, 10 V
  2. Open, 4 A, 0 V
  3. 2.5 $\Omega$, 4 A, 10 V
  4. 2.5 $\Omega$, 4 A, 5 V

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Show answer and explanation

Correct answer: (C) 2.5 $\Omega$, 4 A, 10 V

Explanation

The supply's V-I characteristic is a rectangle with corner at 10 V and 4 A. The load power $VI$ is largest at the corner, where $V=10$ V and $I=4$ A, which gives $P=40$ W. This corresponds to a load resistance of $\frac{10}{4}=2.5\ \Omega$.