Question

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

• A. $100W$
• B. $75W$
• C. $50W$
• D. $25W$

Answer 1

The correct option is D

$25W$

Step 1. Given data:

Rating of electric bulb = $220V$ and $100W$

New voltage = $110V$

Step 2. Formula used:

We know, $P=\raisebox{1ex}{$V^2$}\!\left/ \!\raisebox{-1ex}{$R$}\right.$, where $P=$power, $V=$voltage, $R=$resistance.

Step 3. Calculations:

First, we have to find out the resistance of the bulb by the given rating.

Putting all the known values in the formula above, we get

$R=\raisebox{1ex}{$V^2$}\!\left/ \!\raisebox{-1ex}{$P$}\right.=\raisebox{1ex}{${\left(220\right)}^2$}\!\left/ \!\raisebox{-1ex}{$100$}\right.=484\Omega$

Now we will use this resistance value to find out power at $110V$.

Thus, $P_2=\raisebox{1ex}{$V^2$}\!\left/ \!\raisebox{-1ex}{$R$}\right.=\raisebox{1ex}{${\left(110\right)}^2$}\!\left/ \!\raisebox{-1ex}{$484$}\right.=25W$

Hence, option D is the correct option.