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:

  1. (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

$R _{100}=R _{50}[1+\alpha(100-50)]$

$\Rightarrow 7=5[1+\alpha(50)]$

$\Rightarrow \alpha=\frac{(7-5)}{250}=0.008 /{ }^{\circ} C$