Question

The resistance of a bulb filament is $100\Omega$ at a temperature at ${100}^{o}C$. If its temperature coefficient of resistance be $0.005{/}^{o}C$, then its resistance will become $200\Omega$ at a temperature of

• A. ${300}^{o}C$
• B. ${400}^{o}C$
• C. ${500}^{o}C$
• D. ${200}^{o}C$

Answer 1

The correct option is A ${300}^{o}C$

$\text{Given :}$ $R_{100}=100\Omega$ ,$T_1={100}^{o}C$ ,$R^{\prime }=200\Omega$ , $\alpha =0.005$ per ${}^{o}C$

$\text{Step 1: Relation between resistance and temperature}$

$R=R_0(1+\alpha (T_2-T_1\left)\right)$

where $\alpha$ is the temperature coefficient of resistance.

So, $R^{\prime }=R_{100}(1+\alpha (T_2-T_1\left)\right)$ $....\left(1\right)$

$\text{Step-2: Final temperature}$

Putting values of $R_{100},T_1,R^{\prime },\alpha$ in equation $\left(1\right)$, we get

$200=100(1+0.005(T_2-100\left)\right)$

Or, $T_2-100=200$

$\Rightarrow T_2={300}^{o}C$

Hence, Option A is correct.