First slide

combination of resistance

Question

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

Moderate

A

$0.6 π Ω$
B

$3 Ω$
C

$6 π Ω$
D

$6 Ω$

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
$R_{eq} = \frac{\frac{12 π}{10} \times \frac{12 π}{10}}{\frac{12 π}{10} + \frac{12 π}{10}} = \frac{6 π}{10} = 0 .6 π Ω$

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