Question

A battery of emf 2.1 V and internal resistance is shunted for 5 s by a wire of constant resistance 0.02 $ \Omega $ ,mass 1 g and specific heat 0.1 cal/g/?C. The rise in the temperature of the wire is

• A. $ 10.7{}^\circ C $
• B. $ 21.4{}^\circ C $
• C. $ 107{}^\circ C $
• D. $ 214{}^\circ C $

Answer 1

Answer: (D)

Given, $ E=2.1V,\,r=0.05\,\Omega ,\,t=5s,\,R=0.02\Omega $ $ m=1\,g $ and $ s=0.1\,cal/g{{/}^{o}}C $ $ m\times s\times \Delta T=\frac{{{i}^{2}}Rt}{4.2} $ $ m\times s\times \Delta T=\frac{{{\left( \frac{E}{R+r} \right)}^{2}}Rt}{4.2} $ $ 1\times 0.1\times \Delta T=\left( \frac{2.1\times 2.1}{0.07\times 0.07} \right)\times \frac{0.02\times 5}{4.2} $ $ \Delta \tau =\frac{90}{0.1\times 4.2}=\frac{900}{4.2} $ $ \Delta \tau =214{{\,}^{o}}C $