Question

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-

• A. 1:9
• B. 1:3
• C. 1:18
• D. 1:6

Answer 1

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
$R=\frac{\rho L}{A}\begin{array}{c}\rho =resistivity\\ L=length\\ A=crosssectionalarea\end{array}$
As the material is same, resistivity remains unchanged
$R_A=\frac{\rho 1x}{\prod \left(3y\right)2}{R}_B=\frac{\rho 2x}{\prod \left(1y\right)2}$