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A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure, is

1. 3Ω
2. 6πΩ
3. 6Ω
4. 0.6πΩ

Correct answer: 6Ω

Solution

The total length of the wire is the circumference of the circle, which is 2πr = 2π × 0.1 m = 0.2π m. The total resistance of the wire is R = 12 × 0.2π = 2.4π Ω. Since the wire is bent into a circle, the resistance between diametrically opposite points A and B is the parallel combination of two equal resistances, each being half of the total resistance. Thus, the equivalent resistance is (R/2) || (R/2) = R/4 = (2.4π)/4 = 0.6π Ω.

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