Question

Resistance of tungsten wire at 150${}^{\circ }$C is $133\Omega$. Its resistance temperature coefficient is $0.0045^{\circ }$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)

$\frac{R_{150}}{R_{500}}=\frac{[1+\alpha (150)]}{[1+\alpha (500)]}$
Given, $R_{150}=133\Omega and\alpha =0.045{}^{\circ }C,$
$\therefore \frac{133}{R_{500}}=\frac{1+0.0045\times 150}{1+0.0045\times 500}=\frac{1.675}{3.25}$
$\Rightarrow R_{500}=\frac{3.25\times 133}{1.675}\approx 258\Omega$