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(D) The heat generated in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$. Since the voltage $V$ and time $t$ are constant,the heat gen

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When the wire is divided into four equal parts and all the four parts are connected in parallel.

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(D) The heat generated in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$. Since the voltage $V$ and time $t$ are constant,the heat generated is inversely proportional to the resistance $(H \propto \frac{1}{R})$. To maximize heat,we must minimize the total resistance $R$.Let the resistance of the full wire be $R$. $A$: Resistance = $R/2$.$B$: Two parts of $R/2$ in parallel give $R_{eq} = \frac{(R/2) 	imes (R/2)}{(R/2) + (R/2)} = R/4$.$C$: Resistance = $R$.$D$: Four parts of $R/4$ in parallel give $R_{eq} = \frac{R/4}{4} = R/16$.Comparing the resistances: $R/16 < R/4 < R/2 < R$. Since $R/16$ is the smallest resistance,the heat generated is the largest in case $D$.

You are given a resistance wire of length $50 \,cm$ and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?

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