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)

$266\,\Omega$

Answer 2

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 E (ii) by (i), we get $\frac{R_{t}}{133}=\frac{3.25}{1.675} \approx 2 \Omega$ $\Rightarrow R_{t}=2 \times 133$ $R_{t}=266 \,\Omega$