A long wire is divided into 2 n parts. Then n parts are connected in series and the other n parts are connected in parallel. Both the combinations are given the same voltage supply. The ratio of heat produced in series to the parallel combination will be

Question

A long wire is divided into 2 n parts. Then n parts are connected in series and the other n parts are connected in parallel. Both the combinations are given the same voltage supply. The ratio of heat produced in series to the parallel combination will be, 1 : 1, 1 : n 2, 1 : n 4, n 2 : 1

MARKS App · Accepted Answer

The resistance of each part is r = R / 2 n R s e r i e s = R 2 n × n = R 2 The heat developed in series combination = V 2 R / 2 J s - 1 R p a r a l l e l = r n = R / 2 n n = R 2 n 2 The heat produced in parallel combination = V 2 R / 2 n 2 J s - 1 ∴ H s e r i e s H p a r a l l e l = 2 V 2 R × R 2 n 2 V 2 = 1 : n 2

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