Question

The resistance of a 240 V , 200 W electric bulb when hot is 10 times the resistance when cold.The resistance at room temperature and the temperature coefficient of the filament are
(given working temperature of the filament is 2000${}^0$C)

• A. $28.8\Omega ,4.5\times {10}^{-3}{/}^{0}C$
• B. $14.4\Omega ,4.5\times {10}^{-3}{/}^{0}C$
• C. $28.8\Omega ,3.5\times {10}^{-3}{/}^{0}C$
• D. $14.4\Omega ,3.5\times {10}^{-3}{/}^{0}C$

Answer 1

The correct option is A $28.8\Omega ,4.5\times {10}^{-3}{/}^{0}C$

$R_2=\frac{V^2}{P}$

$R_2=\frac{240\times 240}{200}=288\Omega$

$R_1=\frac{R_2}{10}=28.8\Omega$

$R_2=R_1(1+\alpha \Delta T)$

$R_2=10R_0$

$9=\alpha \Delta T$

As ${2000}^{0}C>>>$ Room temp,

we can take

$\Delta T={2000}^{0}C$

$\alpha =\frac{9}{2000}$

$\therefore \alpha =4.5\times {10}^{-3}$