The ratio of cross-sectional areas of two con | vedclass

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(D) The heat produced per second in a conductor is equal to the power dissipated,given by $P = I^2 R$.Since the wires are made of the same material an

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$2 : 1$

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(D) The heat produced per second in a conductor is equal to the power dissipated,given by $P = I^2 R$.Since the wires are made of the same material and have the same length,the resistance $R$ is given by $R = \rho \frac{l}{A}$.Substituting this into the power formula,we get $P = I^2 \left( \frac{\rho l}{A} \right)$.Since $I$,$\rho$,and $l$ are constant for both wires,we have $P \propto \frac{1}{A}$.Therefore,the ratio of heat produced is $\frac{P_1}{P_2} = \frac{A_2}{A_1}$.Given the ratio of areas $\frac{A_1}{A_2} = \frac{1}{2}$,we have $\frac{A_2}{A_1} = \frac{2}{1}$.Thus,the ratio of heat produced per second is $2 : 1$.

The ratio of cross-sectional areas of two conducting wires made up of the same material and having the same length is $1 : 2$. What will be the ratio of heat produced per second in the wires,when the same current is flowing in them?

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