Question

Two electric bulbs, each designed to operate with a power of 500 W in 220 V line, are connected in series in a 110 V line. The power generated by each bulb will be

• A. 11 W
• B. 312.5 W
• C. 22 W
• D. 31.25 W

Answer 1

The correct option is D 31.25 W

The power consumed in bulbs in series in a 220 V line is
$P=\frac{P_1{P}_2}{P_1+P_2}=\frac{250000}{1000}=250W$
When bulbs are connected in bulbs in series in a 110 V line
$P_1^{\prime }=\frac{\frac{V^2}{4}}{R_1}=\frac{1}{4}P1$
Similarly, $P_2^{\prime }=\frac{1}{4}P2$
Hence,
The power consumed in bulbs in series in a 110 V line is
$P^{\prime }=\frac{P_1^{\prime }{P}_2^{\prime }}{P_1^{\prime }+P_2^{\prime }}$
By putting values of $P_1^{\prime }$ and $P_2^{\prime }$ in last eq. we get ,
$P^{\prime }=\frac{1}{4}P=62.5W$
Therefore, the power consumed in each bulb is $\frac{P^{\prime }}{2}=31.25W$