Question

1. Each of two electric lamps of power 500 W is designed to
work in 220V line. If the lamps are connected in series
and the combination is connected to 110 V line, what will
be the power of each lamp?
Answer: (31.25W)​

Answer 1

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✍ 31.25 W

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EXPLANATION —

The power consumed in lamp in series in a 220 V line is

Given p1 = p2 = 500 w

$p = \: \frac{p1p2}{p1 + p2}$

Putting

$p \: = \frac{500 \times 500}{500 + 500} = \frac{250000}{1000} = 250 \: w$

When bulbs are connected  in lamps in series in a 110 V line 

$p1' = \frac{ \frac{ {v}^{2} }{4} }{R1} = \frac{1}{4} p1$

Simmilerly

$p2' = \frac{1}{4} p2$

Hence,

The power consumed in lamps in series in a 110 V line is

$p' = \frac{p1' \times p2'}{p1' + p2'} = \frac{1}{4} p \: = 62.5 \: w$

Therefore, the power consumed in each lamp is

$= > \frac{p1'}{2} = \frac{62.5}{2} = 31.25 \: w$

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Answer 2

Answer:

Resistance of each bulb As the connection is in series the applied voltage is divided on both the bulbs, so voltage across each is power.