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GATE 2015 EE – Question 57

Electric Circuits · Network solution methods: KCL, KVL, Node and Mesh analysis · 2 marks · Numerical answer

In the given circuit, the parameter $k$ is positive, and the power dissipated in the $2\ \Omega$ resistor is 12.5 W. The value of $k$ is ________.

A 4 V source feeds a $2\ \Omega$ resistor with voltage $V_o$ across it, then a node. From that node there are a $10\ \Omega$ resistor to ground, a dependent current source $kV_o$, and a $5\ \Omega$ resistor leading to a 5 A current source drawing current to ground.

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Correct answer: 0.48 to 0.52

Explanation

The $2\ \Omega$ resistor dissipates 12.5 W, so its current is $\sqrt{\frac{12.5}{2}} = 2.5$ A and $V_o = 5$ V, which means the node is at $4 - 5 = -1$ V. At the node, the current in is $2.5 + kV_o = 2.5 + 5k$, and the current out is $\frac{-1}{10} + 5 = 4.9$ A through the $10\ \Omega$ resistor and the 5 A source branch. So $2.5 + 5k = 4.9$ and $k = 0.48$.