A heater coil is cut into two equal parts and | vedclass

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(A) The heat produced by a heater is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is time,and $R$ is the resistance.Since t

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$2 : 1$

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(A) The heat produced by a heater is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is time,and $R$ is the resistance.Since the voltage $V$ and time $t$ are constant,the heat produced is inversely proportional to the resistance: $H \propto \frac{1}{R}$.When the coil is cut into two equal parts,the resistance of each part becomes $R' = \frac{R}{2}$.Let $H_{Full}$ be the heat produced by the full coil with resistance $R$,and $H_{Half}$ be the heat produced by the half coil with resistance $R/2$.Then,$\frac{H_{Half}}{H_{Full}} = \frac{R}{R_{Half}} = \frac{R}{R/2} = \frac{2}{1}$.Therefore,the ratio of heat produced is $2 : 1$.

$A$ heater coil is cut into two equal parts and only one part is used in the heater. What is the ratio of the heat produced by the half coil to that produced by the original full coil?

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