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)

$258 \Omega$

Answer 2

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