Current Electricity - Result Question 14
15. A wire has a resistance of $3.1 \Omega$ at $30^{\circ} C$ and a resistance $4.5 \Omega$ at $100^{\circ} C$. The temperature coefficient of resistance of the wire
[2001]
(a) $0.008^{\circ} C^{-1}$
(b) $0.0034^{\circ} C^{-1}$
(c) $0.0025^{\circ} C^{-1}$
(d) $0.0012^{\circ} C^{-1}$
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Answer:
Correct Answer: 15. (a)
Solution:
- (a) $R_1=3.1 \Omega$ at $t=30^{\circ} C$
$R_2=4.5 \Omega$ at $t=100^{\circ} C$
We have, $R=R_0(1+\alpha t)$
$\therefore R_1=R_0[1+\alpha(30)]$
$R_2=R_0[1+\alpha(100)]$ $\Rightarrow \frac{R_1}{R_2}=\frac{1+30 \alpha}{1+100 \alpha}$
$\Rightarrow \frac{3.1}{4.5}=\frac{1+30 \alpha}{1+100 \alpha} \Rightarrow \alpha=0.008^{\circ} C^{-1}$
