Two bulbs $A a n d B$ consume same power $P$ when operated at voltages $V_{1} a n d V_{2_{}}$ respectively. If these bulbs are connected in series across a $D C$ source, then:

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3. ratio of power consumed in A and B will be equal to $V_{1} ² : V_{2} ²$

1. ratio of potential differences across A and B will be equal to $V_{1} : V_{2}$

4.ratio of power consumed in $A a n d B$ will be equal

2.ratio of potential differences across A and B will be equal to $V_{1} ² : V_{2} ²$

answer is B, C.

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Detailed Solution

If a bulb having resistance $R$ is used across a voltage $V$ . power consumed in it is given by

$P = \frac{V^{2}}{R} O r, R = \frac{V^{2}}{P}$

Hence, resistances of two bulbs are:
$R_{1} = \frac{{V_{1}}^{2}}{P} O r, R_{2} = \frac{{V_{2}}^{2}}{P}$

If these bulbs are connected in series, the current through them will be same. Hence, potential differences a them will be proportional to their resistances. Therefore, the ratio of potential differences across them will be to equal $R_{1} : R_{2} = {V_{1}}^{2} : {V_{2}}^{2}$

Hence. The option (A) is wrong but the option (B) is correct.

Powers consumed in them will be equal to $P_{1} = i^{2} R_{1} a n d P_{2} = i^{2} R_{2}$

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 (C) is correct but the option (D) is wrong.