Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series

Question 4:

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 –

Solution:

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

Let R_S be the equivalent resistances of the wires if connected in series and R_P  be the equivalent resistances of the wires if connected in parallel

Then R_S=R+R=2R

And 1/ R_P = 1/R +1/R

       1/ R_P = 2/R

Or        R_P =R/2

Now the ratio of heat produced is given by 

 

      = 1/4