Two heater wires of equal length are first co | vedclass

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(D) Let the resistance of each heater wire be $R$. When connected in series,the equivalent resistance is $R_s = R + R = 2R$. When connected in paralle

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$1:4$

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(D) Let the resistance of each heater wire be $R$. When connected in series,the equivalent resistance is $R_s = R + R = 2R$. When connected in parallel,the equivalent resistance is $R_p = \frac{R \cdot R}{R + R} = \frac{R}{2}$. For a constant potential difference $V$,the heat produced $H$ is given by $H = \frac{V^2}{R_{eq}} \cdot t$. Therefore,$H \propto \frac{1}{R_{eq}}$. The ratio of heat produced in series $(H_s)$ to parallel $(H_p)$ is $\frac{H_s}{H_p} = \frac{R_p}{R_s} = \frac{R/2}{2R} = \frac{1}{4}$. Thus,the ratio is $1:4$.

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is

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