CBSE 2025, Set 3

Question

A steady current $I$ is passed through a conductor at room temperature for time $t$. It is observed that its temperature rises by $0.5^\circ	ext{C}$. If $2I$ current is passed through the conductor (at room temperature) for the same duration, the rise in its temperature will be approximately: A). $1.0^\circ	ext{C}$ B). $1.5^\circ	ext{C}$ C). $2.0^\circ	ext{C}$ D). $4.0^\circ	ext{C}$

Edvaya · Accepted Answer

The correct answer is $2.0^\circ	ext{C}$. The heat produced in a conductor is given by Joule's Law of Heating:

$$H = I^2 R t$$

The rise in temperature $\Delta T$ is directly proportional to the heat produced ($H \propto \Delta T$).

Therefore, $\Delta T \propto I^2$.

If the current is doubled ($I' = 2I$), the new temperature rise $\Delta T'$ is:

$$\frac{\Delta T'}{\Delta T} = \left( \frac{2I}{I} ight)^2 = 4$$

$$\Delta T' = 4 	imes 0.5^\circ	ext{C} = \boxed{2.0^\circ	ext{C}}$$

> Heating is proportional to the square of the current passed.

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Physics > Electrostatics And Current Electricity > Current Electricity

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