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)
$\frac{R_{20}}{R_{35}}=\frac{1+20 \alpha}{1+35 \alpha}$
$\frac{25}{25.17}=\frac{1+20 \alpha}{1+35 \alpha}$
$25+875 \alpha=25.17+503.4 \alpha$
$371.6 \alpha=0.17$
$\alpha=\frac{0.17}{317.6}$
$=4.574 \times 10^{4} /{ }^{\circ} C$