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 $R_t=R_0(1+\alpha t)$
$\therefore R_{150}=R_0(1+150\times 0.0045)=133\Omega \dots$ (i)
and $\therefore R_0(1+500\times 0.0045)=R_t\dots$ (ii)
Dividing Eq. (ii) by (i), we get
$\frac{R_t}{133}=\frac{3.25}{1.675}\approx 2\Omega$
$\Rightarrow R_t=2\times 133$
$R_t=266\Omega$