A heating coil can heat the water of a vessel | vedclass

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Question

(A) The heat required to raise the temperature of the water is $Q = mc\Delta T$. Since $m$, $c$, and $\Delta T$ are the same, the required heat $Q$ is

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$60$

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(A) The heat required to raise the temperature of the water is $Q = mc\Delta T$. Since $m$, $c$, and $\Delta T$ are the same, the required heat $Q$ is constant.Power $P$ of a heating coil is given by $P = V^2/R$.For one coil, $P_1 = V^2/R$. The time taken is $t_1 = Q/P_1 = 30\,min$.When two identical coils are connected in series, the equivalent resistance becomes $R_{eq} = R + R = 2R$.The new power is $P_{series} = V^2/R_{eq} = V^2/(2R) = P_1/2$.The new time taken is $t_{series} = Q/P_{series} = Q/(P_1/2) = 2(Q/P_1) = 2t_1$.Substituting $t_1 = 30\,min$, we get $t_{series} = 2 	imes 30 = 60\,min$.

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