A rise of temperature of 4°C is observed in a conductor by passing a current. If the current is tripled, the rise of temperature will be

Question

A rise of temperature of 4°C is observed in a conductor by passing a current. If the current is tripled, the rise of temperature will be (A) 8°C (B) 12°C (C) 16°C (D) 36°C

Tardigrade Admin · Accepted Answer

Heat produced in a wire of resistance R in time t is

H = I^{2} Rt

Heat required to raise the temperature of a wire by

Δ T

is

∴ Q = m s Δ T

Q = H

m s Δ T = I^{2} Rt

or

Δ T \propto I^{2}

∴ \frac{Δ T _{2}}{Δ T _{1}} = (\frac{I _{2}}{I _{1}})^{2}

(\frac{3 I _{1}}{I _{1}}) = 9

Δ T_{2} = Δ T_{1} \times 9 = 4^{\circ} C \times 9

= 3 6^{\circ} C

Q. A rise of temperature of $4^{\circ} C$ is observed in a conductor by passing a current. If the current is tripled, the rise of temperature will be

$8^{\circ} C$

$1 2^{\circ} C$

$1 6^{\circ} C$

$3 6^{\circ} C$

$2 4^{\circ} C$

Q. A rise of temperature of 4∘C is observed in a conductor by passing a current. If the current is tripled, the rise of temperature will be

8∘C

12∘C

16∘C

36∘C

24∘C