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(B) The rate of heat produced in a conductor is given by the formula $P = \frac{V^2}{R}$,where $V$ is the potential difference and $R$ is the resistan

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(B) The rate of heat produced in a conductor is given by the formula $P = \frac{V^2}{R}$,where $V$ is the potential difference and $R$ is the resistance.Since both conductors are connected across the same $dc$ source,the potential difference $V$ remains constant for both.Therefore,the rate of heat produced is inversely proportional to the resistance: $Q \propto \frac{1}{R}$.For the first conductor with resistance $R_1 = R$,the rate of heat is $Q_1 = \frac{V^2}{R}$.For the second conductor with resistance $R_2 = 2R$,the rate of heat is $Q_2 = \frac{V^2}{2R}$.Calculating the ratio $Q_1 / Q_2$:$\frac{Q_1}{Q_2} = \frac{V^2 / R}{V^2 / 2R} = \frac{V^2}{R} 	imes \frac{2R}{V^2} = 2$.Thus,the value of $Q_1 / Q_2$ is $2$.

Two conductors,one having resistance $R$ and another $2R$ are connected in turn across a $dc$ source. If the rate of heat produced in the two conductors is $Q_{1}$ and $Q_{2}$ respectively,what is the value of $Q_{1} / Q_{2}$?

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