Question

The resistance of a wire at room temperature $ 30{}^\circ C $ is found to be $ 10\,\Omega $ . Now to increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is $ 0.002/{}^\circ C $ ]

• A. $ 36{}^\circ C $
• B. $ 83{}^\circ C $
• C. $ 63{}^\circ C $
• D. $ 33{}^\circ C $

Answer 1

The Correct Option is B

$ R={{R}_{0}}(1+\alpha t) $ $ \therefore $ $ {{R}_{0}}(1+30\alpha )=10\,\Omega $ and $ {{R}_{0}}(1+\alpha )=11\,\Omega $ Therefore, $ \frac{11}{10}=\frac{1+\alpha t}{1+30\alpha } $ Or $ 11+330\alpha =10+10\alpha t $ Or $ 11+330\times 0.002=10+10\times 0.002t $ Or $ 11.66=0.02t+10 $ Or $ 0.02t=1.66 $ Or $ t=83{}^\circ C $