JEE MAIN - Physics (2022 - 28th July Evening Shift - No. 23)
An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W.
Answer
14
Explanation
$${P_{100}} = {{{V^2}} \over {{R_{100}}}} \Rightarrow {R_{100}} = {{{V^2}} \over {{P_{100}}}}$$
$${P_{60}} = {{{V^2}} \over {{R_{60}}}} \Rightarrow {R_{60}} = {{{V^2}} \over {{P_{60}}}}$$
$${P_{net}} = {{{V^2}} \over {{R_{60}} + {R_{100}}}} = {{{P_{60}}{P_{100}}} \over {{P_{60}} + {P_{100}}}} = {{60 \times 100} \over {160}} = 37.5$$
This power developed is proportional to resistance.
So, $$P{'_{60}} = {P_{net}} \times {{60} \over {160}} = 37.5 \times {{60} \over {160}} \simeq 14\,W$$
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