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GATE 2017 EE (EE2) – Question 40

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

For the shown source and load, the capacitance C giving maximum transferred load power is

Diagram for GATE 2017 EE (EE2) question 40
  1. 1 nF
  2. 1 μF
  3. 1 mF
  4. 10 mF

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Correct answer: (D) 10 mF

Explanation

The source resistance is 0.5 Ω and ω=100 rad/s. The load has series reactance $\omega L=0.5$ Ω followed by $1\ \Omega$ in parallel with C, whose impedance is $1/(1+j\omega C)$ Ω.

Set ωC=1. The parallel part then becomes $(1-j)/2$ Ω; adding the series inductor gives exactly 0.5+j0 Ω, the conjugate match to the source.

Thus C=1/100=0.01 F=**10 mF, D**, achieving the maximum possible load power.

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