Two wires A and B of the same material have their lengths in the ratio 1:2 and radii in the ratio 3:1. The two wires are connected in parallel across a battery. The ratio of heat produced in A to the heat produced in B for the same time is-

1:9

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1:3

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1:18

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1:6

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Solution

The correct option is C
1:18

let lengths of A and B be 1x and 2x respectively, and radii of A and B be 3y and 1y respectively.
Resistance of a wire is given as
$R = \frac{ρ L}{A} \begin{matrix} ρ = r e s i s t i v i t y L = l e n g t h A = c r o s s s e c t i o n a l a r e a \end{matrix}$
As the material is same, resistivity remains unchanged
$R_{A} = \frac{ρ 1 x}{\prod (3 y) 2} R_{B} = \frac{ρ 2 x}{\prod (1 y) 2}$

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