JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Current Electricity

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A wire of length 25 m and cross-sectional area 0.5 mm^2 having resistivity of 2 x 10^-6 Ohm m is bent into a complete circle. The resistance between diametrically opposite points will be

(A) $12.5Ω$
(B) $50Ω$
(C) $100Ω$
(D) $25Ω$ ✓ Correct

Answer: (D)

Solution

The full wire has resistance

R = \frac{ρ L}{A} = \frac{2 \times 1 0 ^{- 6} \times 25}{0.5 \times 1 0 ^{- 6}} = 100 Ω

. Bent into a circle, two diametrically opposite points split the ring into two equal semicircular arcs, each of resistance

R /2 = 50 Ω

, and these arcs are in parallel between those points:

R_{e q} = \frac{( R /2 ) ( R /2 )}{( R /2 ) + ( R /2 )} = \frac{R}{4} = \frac{100}{4} = 25 Ω.

The resistance between diametrically opposite points is

25 Ω

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Single correct option

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