Question:
A uniform metallic wire has a resistance of $18 \Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is:
Correct Option: 1
Solution:
Resistance, $R \propto l$ so resistance of each side of the
equilateral triangle $=6 \Omega$
Resistance $R_{e q}$ between any two vertices
$\frac{1}{\mathrm{R}_{\mathrm{eq}}}=\frac{1}{12}+\frac{1}{6} \Rightarrow \mathrm{R}_{\text {eq. }}=4 \Omega$