Question

Two bulbs are rated: bulb A 100W, 120 V bulb B 10W, 120 V. If both are connected across a 120V supply, which bulb will consume more energy, When in series? Also calculate the current through each bulb in above cases.

Answer 1

In the case of bulb A, Power: P = `"V"^2/"R"_"A"`

R_A = `"V"^2/"P" = (120 xx 120)/100` = 144 Ω

i.e., Resistance (R_A) of bulb, A = 144 Ω

Similarly resistance R_B of bulb, B = `"V"^2/"P"`

`= (120 xx 120)/10 = 1440` Ω

When the bulb are connected in series:

R = R_A + R_B = 144 + 1440 = 1584 Ω

∴ Current in the circuit `= "V"/"R" = 120/1584 = 0.076` A

Being in series, the same current passes through both the bulbs.

Power consumed in bulbs A = P_A = i² R_A = (0.076)² × 144 = 0.8317 W

Power consumed in bulbs B = P_B = i² R_B = (0.076)² × 144 = 8.317 W

This clearly shows that P_A < P_B i.e., bulb B (10W, 120 V) consumes more energy when these are connected series.