Question

If the current flowing through a fixed resistor is halved, the heat produced in it will become:
(a) double (b) one - half (c) one fourth (d) four times

Answer 1

$H=i^2\times R\times t$

$H$ is the heat produced, $i$ is the current through the wire of resistance $R$ for time $t$.

If $i$ is halved, i.e., $i^{\prime }$ = $\frac{i}{2}$, then

$H^{\prime }=(i^{\prime }{)}^2\times R\times t$

$=\frac{1}{4}\times i^2\times R\times t$

$=\frac{1}{4}H$

so, option (c) is correct.