Question

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

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

Answer 1

The correct option is C ${400}^{\circ }\text{C}$

From the relation between resistance and temperature we know that,

$R_1=R_0(1+\alpha T_1);R_2=R_0(1+\alpha T_2)$

$\therefore \frac{R_2}{R_1}=\frac{1+\alpha T_2}{1+\alpha T_1}\Rightarrow \frac{200}{100}=\frac{1+\alpha T_2}{1+(0.005\times 100)}$

$\Rightarrow 2[1+0.5]=1+5\times {10}^{-3}{T}_2$

$\Rightarrow 2=5\times {10}^{-3}{T}_2$
$\Rightarrow T_2=\frac{2000}{5}={400}^{\circ }\text{C}$

Hence, option (c) is the correct answer.