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, $R_{0}(1+\alpha t)=11\, \Omega$
$\frac{11}{10}=\frac{1+\alpha t}{1+30 \alpha}$
$\Rightarrow 10+(10 \times 0.002 \times t)=11+330 \times 0.002$
$\Rightarrow 0.02 t=1+0.66=1.66$
$\Rightarrow t=\frac{1.66}{0.02}=83^{\circ} C$