A 5°C rise in temperature is observed in a conductor by passing . . .

Question : A 5°C rise in temperature is observed in a conductor by passing a current. If the current is doubled, the rise in temperature of the conductor will be nearly
a) 10°C
b) 20°C
c) 40°C
d) 2.5°C

Doubt by Jayant

Solution :

ΔT₁ = 5°C

ΔT₂ = ?

I₁ = I

I₂ =2I

We know, 
When a current I is passed through a conductor then amount of heat produced will be given as
H=I²Rt
So 
H∝I² — (1)

Also, form Class XI, we know that amount of heat absorbed is given by
H=mcΔT

H∝ΔT— (2)

From (1) and (2)

ΔT∝I²

So
ΔT₂/ΔT₁=(I₂/I1)²

ΔT₂/(5°)=(2I/I)²
ΔT₂ = 4×5°
ΔT₂ = 20° C

Hence, b) would be the correct option.