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.