2 conducting wires of the same materialand 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 shall be?

The wires are of same material, equal lengths and diameters. Hence, the resistance of both wires is same, say R.

 

When they are connected in series:

The voltage across each is V/2 and current is I.

Thus, total heat produced is;

 

 

When they are connected in parallel:

The voltage across them is V and current is I/2

Thus, the heat produced is;

 

 

Thus, the ratio of heat in series and parallel is;

H_s/H_p = 1