Current Electricity - Result Question 17
18. If the resistance of a conductor is $5 \Omega$ at $50^{\circ} C$ and $7 \Omega$ at $100^{\circ} C$, then the mean temperature coefficient of resistance (of the material) is
[1996]
(a) $0.001 /{ }^{\circ} C$
(b) $0.004 /{ }^{\circ} C$
(c) $0.006 /{ }^{\circ} C$
(d) $0.008 /{ }^{\circ} C$
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Answer:
Correct Answer: 18. (d)
Solution:
- (d) Resistance of a material at two different temperatures, $T_1$ and $T_2$ such that $T_2>T$, are related as
$R _{T_2}=R _{T_1}[1+\alpha(T_2-T_1)]$
Using this relation for the present case, we get
$R _{100}=R _{50}[1+\alpha(100-50)]$
$\Rightarrow 7=5[1+\alpha(50)]$
$\Rightarrow \alpha=\frac{(7-5)}{250}=0.008 /{ }^{\circ} C$
