If two bulbs of power 25 W and 100 W respectively each rated at 220 V are connected in series with the supply

Q: If two bulbs of power 25 W and 100 W respectively each rated at 220 V are connected in series with the supply of 440 V. Which bulb will fuse?

(a) 25 W bulb

(b) 100 W bulb

(c) none of these

(d) both

Ans: (a)

Sol:
Resistance of one bulb, R1 = (220)2/25 Ω ;

Resistance of other bulb, R2 = (220)2/100 Ω.

Total resistance when two bulbs are in series,

R = (220)2/25 + (220)2/100 = (220)2/20

current I = V/R = 440/((220)2/20) = 2/11 amp.

Pot. diff. across 25 watt bulb
= IR1 = 2/11 × (220)2/25 = 352 V

Pot. diff. across 100 watt bulb
= IR2 = 2/11 × (220)2/100 = 88 V

Thus, the bulb 25 W will be fused, because it can tolerate only 220 V while the voltage across it is 352 V.