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 $0.002$ per ${}^{\circ }C$].

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

Answer 1

Answer: (B)

We have $R_t=R_0(1+\alpha t)$
Initially, $R_0(1+30\alpha )=10\Omega$
Finally, $R_0(1+\alpha t)=11\Omega$
$\frac{11}{10}=\frac{1+\alpha t}{1+30\alpha }$
$\Rightarrow 10+(10\times 0.002\times t)=11+330\times 0.002$
$\Rightarrow 0.02t=1+0.66=1.66$
$\Rightarrow t=\frac{1.66}{0.02}=83^{\circ }C$