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 $
• E. $ 66{}^\circ C $

Answer 1

Answer: (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 $