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

JEE Main · 2012 · 29 Apr 2012 · Offline · Current Electricity

Two electric 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?

(A)both
(B)100 W
(C)25 W✓ Correct
(D)neither

Answer: (C)

Solution

Each bulb's resistance follows from its rating,

R = \frac{V ^{2}}{P}

, so the

25

W bulb has

\frac{22 0 ^{2}}{25}

and the

100

W bulb has

\frac{22 0 ^{2}}{100}

; the lower-wattage bulb has the larger resistance. In series the same current flows through both, so the supply voltage divides in proportion to resistance and the

25

W bulb takes the greater share of the

440

V. That share exceeds its rated

220

V, so the

25

W bulb is overstressed and fuses, while the

100

W bulb stays within its rating.

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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