Two bulbs A and B consume same power P when operated at voltages V 1 and V 2 respectively. If these bulbs are connected in series across a DC source, then:
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(b, c)
If a bulb having resistance R is used across a voltage V, power consumed in it is given by
P = 
or, R = 
Hence, resistances of two bulbs are:
R 1 = 
or, R = 
If these bulbs are connected in series, the current through them will be same. Hence, potential differences across them will be proportional to their resistances. Therefore, the ratio of potential differences across them will be equal to R 1 : R 2 = V 1 2 : V 2 2 .
Hence. The option is wrong but the option is correct.
Powers consumed in them will be equal to
P 1 = i 2 R 1 and P 2 = i 2 R 2 Since, same current flows through the bulbs, therefore,
P 1 : P 2 = R 1 : R 2 = V 1
2 : V 2 2
Hence, the option is correct but the option is wrong.
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