A wire of resistance \( 18\,\Omega \) is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 4\,\Omega \)
The resistance of a uniform wire is proportional to its length, so each of the three equal sides has one-third of the total resistance.
\( \displaystyle R_{\text{side}} = \frac{18}{3} = 6\,\Omega \)
Between two corners, one side (\( 6\,\Omega \)) is joined in parallel with the other two sides in series (\( 6 + 6 = 12\,\Omega \)).
\( \displaystyle R_{\mathrm{eq}} = \frac{6 \times 12}{6 + 12} = \frac{72}{18} = 4\,\Omega \)