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A wire has a resistance of 12 ohm. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is

1. 9 ohm
2. 12 ohm
3. 6 ohm
4. 8/3 ohm

Correct answer: 8/3 ohm

Solution

The 12 ohm wire is divided equally into three sides, so each side has resistance 4 ohm. Between any two corners, one path is 4 ohm and the other path is 8 ohm in series. These two paths are in parallel, giving \(R_{eq} = \frac{4 \times 8}{4+8} = \frac{8}{3}\,\Omega\).

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