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Two conducting wires of the same material of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of heat produced in series to parallel combinations would be
1. 1 ∶ 2
2. 2 ∶ 1
3. 1 ∶ 4
4. 4 ∶ 1

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Best answer
Correct Answer - Option 4 : 4 ∶ 1

The correct answer is 1 : 4.

Explanation:

Given,

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.

For series combination

Total resistance R = R1 + R2 + …………

So calculating the series resistance in the given combination we get

⇒Rp =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.

NOTE: Heat is directly proportional to resistance, if we change the resistance then the heat also changes.

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