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  4. A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance (in Ω) between any two vertices of the triangle is:

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Q. A uniform metallic wire has a resistance of $18\,\Omega$ and is bent into an equilateral triangle. Then, the resistance (in $\Omega$) between any two vertices of the triangle is:

Current Electricity

Solution:

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Resistance, $R \propto l$ so resistance of each side of the
equilateral triangle $= 6\,\Omega$
Resistance $R_{eq}$ between any two vertices
$\frac{1}{R_{eq}} = \frac{1}{12} + \frac{1}{6}$
$\Rightarrow R_{eq.} = 4\Omega$