Question

A coil of resistance 100 Ω is connected across a battery of emf 6.0 V. Assume that the heat developed in the coil is used to raise its temperature. If the heat capacity of the coil is 4.0 J K⁻¹, how long will it take to raise the temperature of the coil by 15°C?

Answer 1

Given:
Resistance of the coil, R = 100 Ω,
Emf of the battery, V = 6 V,
Change in temperature, ∆T = 15°C
Heat produced across the coil,
$H=\frac{V^2}{R}t$
This heat produced is used to increase the temperature of the coil.
$$\begin{gathered} \Rightarrow H=c∆T \\ \Rightarrow \frac{V^2}{R}t=c∆T \\ \Rightarrow \frac{36}{100}t=4\times 15 \\ \Rightarrow t=\frac{6000}{36}=166.7\mathrm{s}=2.8\min \end{gathered}$$