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

Answer: (B)

$83{}^\circ C$

Answer 2

$R={{R}_{0}}(1+\alpha t)$ $\therefore$ ${{R}_{0}}(1+30\alpha )=10\,\Omega$ 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 $t=83{}^\circ C$