Question

A coil has resistance $25.00\Omega$. and $25.17\Omega$ at $20^{\circ }C$ and $35^{\circ }C$ respectively. What is the temperature coefficient of resistance?

• A. $4.545\times 10^{-4}/{}^{o}C$
• B. $4.545\times 10^{-3}/{}^{\circ }C$
• C. $4.545\times 10^{-2}/{}^{o}C$
• D. $4.545\times 10^{-5}/{}^{o}C$

Answer 1

Answer: (A)

We have, $R_t=R_0(1+\alpha t)$
$R_{20}=R_0(1+20\alpha )$...(i)
$R_{35}=R_0(1+35\alpha )$..(ii)
From Eqs. (i) and (ii)
$\frac{R_{20}}{R_{35}}=\frac{1+20\alpha }{1+35\alpha }$
$\frac{25}{25.17}=\frac{1+20\alpha }{1+35\alpha }$
$25+875\alpha =25.17+503.4\alpha$
$371.6\alpha =0.17$
$\alpha =\frac{0.17}{317.6}$
$=4.574\times 10^4/{}^{\circ }C$