Question

The resistance of the bulb filament is $100\Omega$ at a temperature of ${100}^{\circ }C$. If its temperature co-efficient of resistance be $0.005$ per ${}^{\circ }C$, its resistance will become $200\Omega$ at a temperature

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

Answer 1

The correct option is A ${300}^{\circ }C$

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

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

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

OR $T_2-100=200$ $⟹T_2={300}^{o}C$