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GATE 2017 EE – Question 29

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

The equivalent resistance between the terminals A and B is ________ $\Omega$.

A resistor network between terminals A and B. A $1\ \Omega$ resistor is in series with A and a $0.8\ \Omega$ resistor is in series with B. In between there are a $2\ \Omega$ resistor along the top, a $3\ \Omega$ resistor at the left, a $6\ \Omega$ resistor and a $3\ \Omega$ resistor in a diagonal arrangement, a $6\ \Omega$ resistor at the right, and a $1\ \Omega$ resistor with another $1\ \Omega$ resistor in a loop on the far right.

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Correct answer: 2.9 to 3.1

Explanation

The $1\ \Omega$ and $0.8\ \Omega$ resistors at the terminals add up to $1.8\ \Omega$ in series. Following the official key, the rest of the network between them is equivalent to about $1.2\ \Omega$, which is the $2\ \Omega$ and $3\ \Omega$ resistors in parallel ($\frac{2 \times 3}{2 + 3} = 1.2\ \Omega$). The total is $1.8 + 1.2 = 3\ \Omega$.