Question

The resistance of tungsten filament at $150^{\circ} C$ is $133 \Omega$ what will be its resistance at $500^{\circ} C$ ?
The temperature coefficient of resistance of tungsten is $0.0045 /{ }^{\circ} C$.

• A. $ 366\,\Omega $
• B. $ 69\,\Omega $
• C. $ 266\,\Omega $
• D. $ 109\,\Omega $

Answer 1

Answer: (C)

It $R_{t}$ be resistance att ${ }^{\circ} C$ and $R_{0}$ be at $0^{\circ} C$,
and a be temperature coefficient of resistance,
then $R_{t}=R_{0}(1+\alpha t)$
$\therefore R_{150}=R_{0}(1+150 \times 0.0045)=133 \Omega \ldots$ (i)
and $\therefore R_{0}(1+500 \times 0.0045)=R_{t} \ldots$ (ii)
Dividing Eq. (ii) by (i), we get
$\frac{R_{t}}{133}=\frac{3.25}{1.675} \approx 2 \Omega$
$\Rightarrow R_{t}=2 \times 133$
$R_{t}=266 \,\Omega$