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  4. A 5° C rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately

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Q. A $5^{\circ} C$ rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately

AIPMTAIPMT 1998Current Electricity

Solution:

$H=I^{2} R t=m s \Delta T$
$\frac{I_{1}^{2}}{I_{2}^{2}}=\frac{\Delta T_{1}}{\Delta T_{2}}$
or, $\Delta T_{2}=\frac{\Delta T_{1} I_{2}^{2}}{I_{1}^{2}}$
$\Delta T_{2}=5 \times \frac{\left(2 I_{1}\right)^{2}}{I_{1}^{2}}=20 ; $
$ \Delta T_{2}=20^{\circ} C .$