Question

An electric bulb is rated $220V$ and $100W.$ When it is operated at $110V,$ the power consumed will be

• A. $100\text{W}$
• B. $75\text{W}$
• C. $50\text{W}$
• D. $25\text{W}$

Answer 1

The correct option is D $25\text{W}$

Power consumed by the electric bulb, $P=\frac{V^2}{R}$, where $V$ is the potential difference and $R$ is the electrical resistance.
Given for 1st case:
Voltage $V_1=220V$
and power consumed by bulb $P_1=100W,$
In the 2nd case:
Voltage of the bulb, $V_2=110V$
Power consumed by the bulb = $P_2$
Since the resistance is the same as it is the same bulb
$\frac{P_1}{P_2}=\frac{(V_1{)}^2}{(V_2{)}^2}$
$\frac{100}{P_2}=\frac{(220{)}^2}{(110{)}^2}$
$P_2=\frac{100\times (110{)}^2}{(220{)}^2}=25W$
Power consumed when the bulb is operated at 110V = 25W