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A network of resistors is connected between terminals A and B. The network consists of five resistors each of resistance R arranged so that three resistors form a triangle (each side R) and two additional resistors of resistance R each connect the midpoints of two sides of the triangle to points A and B respectively. Find the equivalent resistance between A and B.

1. R/11
2. 12R/11
3. R
4. 4R

Correct answer: 12R/11

Solution

By applying Kirchhoff's current law at each node and using symmetry of the resistor network, the equivalent resistance works out to 12R/11. This is a classic result for a specific five-resistor bridge-like arrangement where direct application of KCL gives the numerator-denominator relationship of 12 and 11.

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