Question

The resistance of a bulb filament is $100\, \Omega$ at a temperature of $100^°C$. If its temperature coefficient of resistance be $0.005$ per $^°C$, its resistance will become $200\,\Omega$ at a temperature of:

• A. $300^°C$
• B. $400^°C$
• C. $500^°C$
• D. $200^°C$

Answer 1

Answer: (B)

Let resistance of bulb filament is $R_0$ at $0^°C$ then from expression
$R_{\theta}=R_{0}\left[1+\alpha\Delta\theta\right]$
we have, $100=R_{0}\left[1+0.005\times100\right]$
and $200=R_{0}\left[1+0.005\times x\right]$
where $x$ is temperature in $^°C$ at which resistance become $200\,\Omega$.
Dividing the above two equations
$\frac{200}{100}=\frac{1+0.005x}{1+0.005\times100} \Rightarrow x=400^°C$