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
$\frac{133}{R_{500}}=\frac{1+0.0045\times 150}{1+0.0045\times 500}$
$=\frac{1.675}{3.25}$
$\Rightarrow R_{500}=\frac{3.25\times 133}{1.675}\approx 258\Omega$