Question

A wire has resistance of $3.1 \,\Omega $ at $30^{\circ} \, C$ and $4.5\, \Omega $ at $100^{\circ} C$ . The temperature coefficient of resistance of the wire is

• A. $0.0012^{\circ} C^{-1}$
• B. $0.0024^{\circ} C^{-1}$
• C. $0.0032^{\circ} C^{-1}$
• D. $0.0064^{\circ} C^{-1}$

Answer 1

Answer: (D)

Given,
$R _{2}= 4 . 5 \Omega$
$R _{1}= 3 . 1 \Omega$
$T _{1}= 3 0 ^{\circ} C$
$T _{2}= 1 0 0 ^{\circ} C$
$T _{2}- T _{1}=( 1 0 0 - 3 0 )^{\circ} C$
$= 7 0 ^{\circ}$
$\Rightarrow 4.5=3.1[1+\alpha(70)]$
$\Rightarrow 70 \alpha=\frac{4.5}{3.1}-1$
$\alpha=\frac{4.5-3.1}{3.1 \times 70}$
$\alpha=6.45 \times 10^{-3}$
$\alpha=0.0064^{\circ} C ^{-1}$