Question

Two conducting wires of the same material and of equal lengths and equal diameter
are first connected in series and then parallel in a circuit across the same potential
dience. The mtio of heat produced in series and parallel combination would be
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Answer 1

Answer:

Let us make the following assumptions to calculate the ratio of heat produced in series and parallel combination

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

Formula

For series combination

Total resistance R = R1 + R2 + …………..

So calculating the series resistance in the given combination we get

RS =R+R=2R————-(i)

For parallel combination

Total resistance 1/R = 1/R1 + 1/R2 + …………..

So calculating the parallel resistance in the given combination we get

1/ RP = 1/R +1/R

1/ RP = 2/R

RP =R/2———-(ii)

To find the ratio we will combine equations (i) and (ii) we get

Rp/Rs = (R/2)/2R = 1/4

The ratio of heat produced is 1/4

Answer

Hence the ratio of the resistances is 1/4