Question

An electric bulb is rated $(100\text{W},220\text{V})$. If it consumes $25\text{W}$ power, then the applied voltage across the bulb is

• A. $110\text{V}$
• B. $50\text{V}$
• C. $250\text{V}$
• D. $180\text{V}$

Answer 1

The correct option is A $110\text{V}$

Rated power of electric bulb, $P=100\text{W}$
Voltage applied across bulb, $V=220\text{V}$
Let $V\text{'}$ be the applied voltage across bulb, when it consumes power $\left(P\text{'}\right)25\text{W}$.
Now, $P=\frac{V^2}{R}$ ... (i)
$P^{\prime }=\frac{(V^{\prime }{)}^2}{R}$ ... (ii)
Using (i) and (ii)
$V^{\prime }=\left(\sqrt{\frac{P^{\prime }}{P}}\right)\times V$
$=\left(\sqrt{\frac{25}{100}}\right)\times 220$
$=110\text{V}$
Hence, the correct answer is option (a).