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Physics-

General

Easy

Question

In the circuit as shown in the figure, the heat produced by 6 ohm resistance due to current flowing in it is 60 calorie per second. The heat generated across 3 ohm resistance per second will be

30 calorie
60 calorie
100 calorie
120 calorie

The correct answer is: 120 calorie

Resistance of upper branch $R subscript 1 end subscript equals 2 plus 3 equals 5 capital omega$
Resistance of lower branch $R subscript 2 end subscript equals 4 plus 6 equals 10 capital omega$
Hence $fraction numerator i subscript 1 end subscript over denominator i subscript 2 end subscript end fraction equals fraction numerator R subscript 2 end subscript over denominator R subscript 1 end subscript end fraction equals fraction numerator 10 over denominator 5 end fraction equals 2$
$fraction numerator text Heat generated across 3 end text capital omega blank left parenthesis H subscript 1 end subscript right parenthesis over denominator text Heat generated across 6 end text capital omega blank left parenthesis H subscript 2 end subscript right parenthesis end fraction equals fraction numerator i subscript 1 end subscript superscript 2 end superscript cross times 3 over denominator i subscript 2 end subscript superscript 2 end superscript cross times 6 end fraction equals fraction numerator 4 over denominator 2 end fraction equals 2$
\ Heat generated across 3 W = 120 cal/sec

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