The applied potential difference across a giv | vedclass

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(B) The heat produced per second in a resistor is given by the power formula $P = \frac{V^2}{R}$,where $V$ is the potential difference and $R$ is the

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$4$

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(B) The heat produced per second in a resistor is given by the power formula $P = \frac{V^2}{R}$,where $V$ is the potential difference and $R$ is the resistance.Since the resistance $R$ remains constant,the heat produced per second is directly proportional to the square of the potential difference,i.e.,$P \propto V^2$.If the heat produced per second increases by a factor of $16$,then $P' = 16P$.Substituting this into the proportionality,we get $16P \propto (V')^2$.Since $P \propto V^2$,we have $16V^2 = (V')^2$.Taking the square root of both sides,we get $V' = 4V$.Therefore,the applied potential difference changes by a factor of $4$.

The applied potential difference across a given resistor is altered so that the heat produced per second increases by a factor of $16.$ By what factor does the applied potential difference change?

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