Two bulbs rated 200 W, 220 V and 100 W, 220 V are connected in series. Combination is connected to 220 V supply. Power consumed by the circuit is?

Question

Two bulbs rated 200 W, 220 V and 100 W, 220 V are connected in series. Combination is connected to 220 V supply. Power consumed by the circuit is? (A) 80 W (B) 67 W (C) 76 W (D) 65 W

Tardigrade Admin · Accepted Answer

Effective resistance in series is sum of individual resistances. Power consumed by a bulb, potential difference across which is V, is

P = \frac{V ^{2}}{R}

where, R is resultant resistance. In series combination,

R = R_{1} + R_{2}

∴

P = \frac{V ^{2}}{R _{1} + R _{2}} = \frac{V ^{2}}{\frac{V ^{2}}{P _{1}} + \frac{V ^{2}}{P _{2}}}

\Rightarrow

\frac{1}{P} = \frac{1}{P _{1}} + \frac{1}{P _{2}}

= \frac{1}{200} + \frac{1}{100}

\Rightarrow

P = 67 W

Q. Two bulbs rated 200W, 220V and 100W, 220V are connected in series. Combination is connected to 220V supply. Power consumed by the circuit is?

80 W

67 W

76 W

65 W

Q. Two bulbs rated $200 W$ , $220 V$ and $100 W$ , $220 V$ are connected in series. Combination is connected to $220 V$ supply. Power consumed by the circuit is?