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GATE 2015 EC – Question 42

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Numerical answer

In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.

A source $4\angle 0°$ V (rms) in series with a $2\ \Omega$ resistor feeds a $j2\ \Omega$ inductor in parallel with the load resistor $R_L$.

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Correct answer: 1.6 to 1.7

Explanation

The load is purely resistive, so the maximum power goes to $R_L = |Z_{th}|$. The Thevenin impedance seen by the load is $2 \parallel j2 = 1 + j$, with magnitude $\sqrt{2}$. The Thevenin voltage magnitude is $4 \times \frac{|j2|}{|2 + j2|} = 2\sqrt{2}$ V. The power is $\frac{|V_{th}|^2 R_L}{|Z_{th} + R_L|^2} = \frac{8 \times 1.414}{(1 + 1.414)^2 + 1} = \frac{11.31}{6.83} = 1.66$ W.