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Q.

A wire of resistance $12 Ω m^{- 1}$ is bent to form a complete circle of radius 10 cm. The resistance between is two diametrically opposite points, A and B as shown in the figure, is

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a

$0.6 π Ω$

b

$3 Ω$

c

$6 π Ω$

d

$6 Ω$

answer is A.

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Detailed Solution

Circumference of circle $= 2 \times π \frac{10}{100} = \frac{2 π}{10} = \frac{π}{5}$

Resistance of wire $= 12 \times \frac{π}{5} = \frac{12 π}{5}$

Resistance of each section $= \frac{12 π}{10} Ω$

$∴$ Equivalent resistance $R_{e q} = \frac{\frac{12 π}{10} \times \frac{12 π}{10}}{\frac{12 π}{10} + \frac{12 π}{10}} = \frac{6 π}{10} = 0.6 π Ω$

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A wire of resistance 12Ωm−1 is bent to form a complete circle of radius 10 cm. The resistance between is two diametrically opposite points, A and B as shown in the figure, is