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JEE Main 2022 (29 Jun, Shift 1) · Electrical Power & Heating Effect

Electrical Power & Heating Effect question from JEE Main 2022 (29 Jun, Shift 1)

Q27JEE Main 2022 · 29 JUN · SHIFT 1Medium

Electrical Power & Heating Effect

Two coils require 20 minutes and 60 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.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

Same $V$ and same heat: $H = \frac{V^2}{R}t$ , so $t \propto R$ .
In parallel $R_p = \frac{R_1R_2}{R_1 + R_2}$ , so $t_p = \frac{t_1t_2}{t_1 + t_2}$ .
$t_p = \frac{20 \times 60}{80} = 15$ min.

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