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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?
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Solution
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.
\[\Rightarrow H = c ∆ T\]
\[ \Rightarrow \frac{V^2}{R}t = c ∆ T\]
\[ \Rightarrow \frac{36}{100}t = 4 \times 15\]
\[ \Rightarrow t = \frac{6000}{36} = 166 . 7 s = 2 . 8 \min\]
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