Q. Two bulbs of 500 W and 200 W are manufactured to operate on 220 V line. The ratio of heat produced in 500 W and 200 W, in two cases, when firstly they are connected in parallel and secondly in series will be
A) $\frac{5}{2}:\frac{2}{5}$
B) $\frac{5}{2}:\frac{5}{2}$
C) $\frac{2}{5}:\frac{5}{2}$
D) $\frac{2}{5}:\frac{2}{5}$
Explanation
(a) In parallel, $\frac{H_{1}}{H_{2}} = \frac{P_{1}t}{P_{2}t} = \frac{P_{1}}{P_{2}} = \frac{500}{200} = \frac{5}{2}$
In series, $\frac{H_{1}}{H_{2}} = \frac{I^{2}R_{1}t}{I^{2}R_{2}t} = \frac{R_{1}}{R_{2}} = \frac{V^{2}/P_{1}}{V^{2}/P_{2}}$
$= \frac{P_{2}}{P_{1}} = \frac{200}{500} = \frac{2}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.