Question

The resistance of a wire at $20C$ is $20$ ohms and at $500C$ is $60$ ohms. At which temperature its resistance will be $25$ ohm?

• A. ${80}^{o}C$
• B. ${70}^{o}C$
• C. ${60}^{o}C$
• D. ${50}^{o}C$

Answer 1

Answer: (A)

${80}^{o}C$

Given : $R_T=60$ ohms @ $T={500}^{o}C$

Also, $R_{T^{\prime }}=20$ ohms @ $T^{\prime }={20}^{o}C$

Resistance at a given temperature $R_T=R_{T^{\prime }}[1+\alpha (T-T^{\prime }\left)\right]$

$\therefore$ $60=20[1+\alpha (500-20\left)\right]$

$⟹$ $\alpha =\frac{2}{480}=0.00417$

Let resistance of wire is $25$ ohm at temperature $T^{\prime \prime }$.

$\therefore$ $R_{T^{\prime \prime }}=R_{T^{\prime }}[1+\alpha (T^{\prime \prime }-T^{\prime }\left)\right]$

OR $25=20[1+(0.00417\left)\right(T^{\prime \prime }-20\left)\right]$

$⟹$ $T^{\prime \prime }={80}^{o}C$