Question

Two conducting wires of the same material and of equal lengths and equal diameters

are first connected in series and then parallel in a circuit across the same potential

difference. The ratio of heat produced in series and parallel combinations would be –

(a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1​

Answer 1

Answer:

option D 4:1

We know that

Heat produced in the circuit is inversely proportional to the resistance R.

Let us assume the equivalent resistances of the wires if connected in series as Rs

Let us assume the equivalent resistances of the wires if connected in parallel as Rp

So RS =R+R=2R

1/ RP = 1/R +1/R

1/ RP = 2/R

RP =R/2

The ratio of heat produced is 2R / R/2 = 1/4

Hence the ratio of the resistances is 1:4

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