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GATE 2016 EC – Question 44

Networks, Signals and Systems · Circuit Analysis · 2 marks · Numerical answer

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor $R$ is ________

A 5 V source feeds a $3\ \text{k}\Omega$ resistor in series with a $2\ \text{k}\Omega$ resistor, and $v_0$ is the voltage across the $2\ \text{k}\Omega$ resistor. A dependent voltage source $100\,v_0$ in series with a $10\ \text{k}\Omega$ resistor feeds a $40\ \text{k}\Omega$ resistor in parallel with the load $R$.

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Correct answer: 0.78 to 0.82

Explanation

The first loop is a voltage divider, so $v_0 = 5 \times \frac{2}{3 + 2} = 2$ V and the dependent source is $100 \times 2 = 200$ V. Looking into the output side from the load, the Thevenin voltage is $200 \times \frac{40}{10 + 40} = 160$ V and the Thevenin resistance is $10 \parallel 40 = 8\ \text{k}\Omega$. The maximum power is $\frac{V_{th}^2}{4R_{th}} = \frac{160^2}{4 \times 8000} = 0.8$ W.