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

Answers (1)

If resistors are connected in parallel, the net resistance is given as 

                 frac1R_p=frac1R_1+frac1R_2

        Rightarrow frac1R_p=frac1R+frac1R

         Rightarrow frac1R_p=frac2R

          Rightarrow R_p=fracR2

If resistors are connected in series, the net resistance is given as 

                      Rightarrow R_s=R_1+R_2=R+R=2R

Heat produced = H = fracV^2Rt

fracH_sH_p=fracfracV^2t2RfracV^2tfracR2

Rightarrow fracH_sH_p=frac14

Rightarrow H_s:H_p=1:4

Thus, option C is correct.

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