Current Electricity

JEE Main level, numerical answer, medium

242 of 380

Question 242 of 380

Two coils require 2020 minutes and 6060 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be _____ min⁡\min.

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Answer: 15

If HH is the heat required to heat the water, then
P1×60=H⇒P1=H60{P}_{1}\times 60=H\Rightarrow {P}_{1}=\dfrac{H}{60} and P2×20=H⇒P2=H20{P}_{2}\times 20=H\Rightarrow {P}_{2}=\dfrac{H}{20}
When the coils are connected in parallel their powers will get added. If the required time now is tt, then
(P1+P2)t=H⇒t=HH60+H20=15min⁡\left({P}_{1}+{P}_{2}\right)t=H \Rightarrow t=\dfrac{H}{\dfrac{H}{60}+\dfrac{H}{20}}=15\min

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