Q. Three electric bulbs with same voltage ratings of 110 volts but wattage ratings of 40, 60 and 100 watts respectively are connected in series across a 220 volt supply line. If their brightness are $B_{1},B_{2},B_{3}$ respectively, then
A) $B_{1} > B_{2} > B_{3}$
B) $B_{1} > B_{2} < B_{3}$
C) $B_{1} = B_{2} = B_{3}$
D) Bulbs will burn out due to the high voltage supply
Explanation
(a) Resistance of a bulb $= \ \frac{(Rated\ voltage)^{2}}{Rated\ power}$
For a given voltage$,\ R \propto \frac{1}{P}$
$\therefore R_{40} > R_{60} > R_{100}$
Rate of heat produced, $H = I^{2}R$
When the bulbs are connected in series, the current flowing through each bulb is same
$\therefore H \propto R\ .$ As$\ R_{40} > R_{60} > R_{100}$
$\therefore H_{40} > H_{60} > H_{100} \Rightarrow B_{1} > B_{2} > B_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.