Question

Resistance of tungsten wire at $150^{\circ}C$ is $133\Omega$ . Its resistance temperature coefficient is $0045^{\circ}/C$ . The resistance of the wire at $500^{\circ}C$ will be

• A. $ 180\,\Omega $
• B. $ 225\,\Omega $
• C. $ 258\,\Omega $
• D. $ 317\,\Omega $

Answer 1

Answer: (C)

$\frac{R_{150}}{R_{500}}=\frac{[1+\alpha(150)]}{[1+\alpha(500)]}$
Putting $R_{150}=133 \Omega$ and
$\alpha=0.0045 /{ }^{\circ} C$,
we have
$\frac{133}{R_{500}}=\frac{1+0.0045 \times 150}{1+0.0045 \times 500}$
$=\frac{1.675}{3.25}$
$\Rightarrow R_{500}=\frac{3.25 \times 133}{1.675} \approx 258\, \Omega$