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GATE 2016 EE – Question 28

Electric Circuits · Network solution methods: KCL, KVL, Node and Mesh analysis · 1 mark · Numerical answer

In the given circuit, the current supplied by the battery, in ampere, is ________.

A 1 V battery feeds a 1 Ω resistor carrying current $I_1$ into a node. From that node, a dependent current source of value $I_2$ points down to ground, and a second 1 Ω resistor leads to a 1 Ω load carrying current $I_2$ to ground.

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Show answer and explanation

Correct answer: 0.49 to 0.51

Explanation

Let the node voltage be $V$. Then $I_1 = 1 - V$, and the current through the two series 1 Ω resistors on the right is $I_2 = \frac{V}{2}$. The dependent source also draws $I_2$. KCL at the node gives $I_1 = I_2 + I_2 = 2I_2 = V$. So $1 - V = V$, which gives $V = 0.5$ V and $I_1 = 0.5$ A.