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)

$400^?C$

Answer 2

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 $\frac{200}{100}=\frac{1+0.005x}{1+0.005\times100} \Rightarrow x=400^?C$