A wire of uniform cross section 'A', length 'l' and resistance 'R' is bent into a complete circle. The equivalent resistance between any two diametrically opposite points will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{R}{4} \)
The resistance of a wire is proportional to its length. Two diametrically opposite points divide the circular wire into two equal semicircles, each of resistance \( R/2 \). Between those two points the semicircles are connected in parallel.
\( \displaystyle R_{\mathrm{eq}} = \frac{(R/2)\times(R/2)}{R/2 + R/2} = \frac{R^{2}/4}{R} = \frac{R}{4} \)