Two electic bulbs marked `25 W -220 V` and `100 W - 220 V` are connected in series to a 440 V supply. Which of the bulbs will fuse?

Options

A. Both
B. 100 W
C. 25 W
D. Neither

Answer

C

Explanation

(c) The current upto which bulb of marked `25 W - 220 V`, will
not fuse `I_1 = W_1/V_1 = 25/220 Amp`
Similarly, `I_2 = W_2/V_2 = 100/220 Amp`
The current flowing through the circuit

`I = (440/(R_(eff))), R_(eff) = R_1 + R_2`
`R_1 = (V_(1)^(2))/(P_1) = (220)^2/(25) , R_2 = (V_(2)^(2))/P = (220)^2/100`
I = (440)/((220)^2/25 + (220)^2/100) = (440/((220^2)[1/25 + 1/100]))`
`I = 40/220 Amp`
`.: I_1 (=25/220A) lt I(=40/220A) lt I_2(=100/200A)`
Thus the bulb marked 25 W - 220 will fuse.