Question

An electric bulb is rated (50W, 200 V). If it is operated at 100 V, then find the power consumed by it.

Answer 1

(50W,200V) means the bulb will consume 50 W power when it is connected to a supply of 200 Volts.
Rated Power (P)=50W
Rated Voltage (V)=200V
we known
$P=\frac{V^2}{R}$
So,
Resistance of the bulb
$R=\frac{V^2}{P}$
$R=\frac{{200}^2}{50}$

$R=\frac{200\times 200}{50}$

$R=800\Omega$

Resistance of the bulb remains same for any applied voltage.
​​​​
power ,$P=\frac{V^2}{R}$
Applied voltage = 100 V
So,

$P=\frac{{100}^2}{800}$

$P=\frac{100\times 100}{800}$

$P=12.5W$