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, $100=R_0\left[1+0.005\times 100\right]$
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
$\frac{200}{100}=\frac{1+0.005x}{1+0.005\times 100}\Rightarrow x=400^{°}C$