Question

Two bulbs `A and B` are rated `100W - 120 V and 10 W - 120 V` respectively. They are connected across a `120 V` source in series. Which will consume more energy ?

Answer 1

Resistance of the bulb A (rating `100 W - 120 V`), i.e.,
`R_1 = (V^2)/(P_1) = ((120 V)^2)/(100 W) = 144 Omega` `(P = V^2 //R)`
Resistance of the bulb B (rating `10 W, 120 V`), i.e., `R_2 = (V^2)/(P_2) = ((120 V)^2)/(10 W) = 1440 Omega`
When the bulbs are connected in series, total resistance of the combination,
`R = R_1 + R_2 = 144 Omega + 1440 Omega = 1584 Omega`
When these bulbs in series are connected across `120 V`, current in the circuit, i.e.,
`I = (V)/(R ) = (120 V)/(1584 Omega) = 0.076 A`
This obviously is the current through each bulb as these are in series.
Power consumed by the bulb A, i.e., `P_1 = I^2 R_1 = (0.076 A)^2 (144 Omega) = 0.832 W`
Power consumed by the bulb B, i.e., `P_2 = I^2 R_2 = (0.076 A)^2 (1440 Omega) = 8.32 W`
Hence, the bulb B (rated `10 W - 120 V`) consumes more energy than the bulb A (rated `100 W - 120 W`) when there are connected in series.