Question 588: Thermodynamics & KTG

Question

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.

Accepted Answer

$$H = {{{V^2}} \over R}\,.\,\Delta t$$
$$ \Rightarrow H = {{{V^2}} \over {{R_1}}}\,.\,20 = {{{V^2}} \over {{R_2}}}\,.\,60$$ ..... (i)
Also, $$H = {{{V^2}} \over {\left[ {{{{R_1}{R_2}} \over {{R_1} + {R_2}}}} \right]}}\,.\,\Delta t$$
$$ = {4 \over 3}\,.\,{{{V^2}} \over {{R_1}}}\,.\,\Delta t$$ [$$\because$$ $${R_2} = 3{R_1}$$]
$$ \Rightarrow \Delta t = 15$$

Thermodynamics & KTG

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