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

Options

A. none
B. both
C. 100W
D. 25W

Answer

D

Explanation

Let `R_(1)` be the resistance of the 25W bulb and `R_(2)` the resistance of 100W bulb.
`R_(2) (V^(2))/(P) = (220 xx 220)/(100) = R` (say)
`R_(1) = (V^(2))/(P) = (220 xx 220)/(25) = 4R`
Let `V_(1)` be the potential difference across 25W bulb and `V_(2)` is the potential difference across 100W bulb when 440V is applied. In a series combination the same current passes through both the resistors and hence potential difference across them is directly proportional to their resistance. So we can write the potential differences as follows:
`V_(1) = (R_(1))/(R_(1) +R_(2)) V= (4R)/(4R+ R) xx 440 =(4)/(5) xx 440 = 352` volts
`V_(2) = 440-352 = 88` volts
We can see that the voltage across 25W bulb is 352V which is more than the rated voltage of 220V. Thus, the bulb os 25W bulb will fuse and option (d) is correct.