Two conducting wires have equal lengths 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:

Two conducting wires have equal lengths equal diameters are first conn

1.	Two conducting wires have equal lengths 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:
Answer» `1:2` `2:1` `1:4` `4:1` Solution :As Two conducting wires have equal lengths equal diameters (i.e., equal CROSS section wire and are of the same MATERIAL, their resistances are same. Thus, `R_1=R_2=R` (say). In SERIES arrangement, `R_s=R_1+R_2=2R` and in parallel arrangement `1/R_p=1/R_1+1/R_2=1/R+1/R=2/R or R_p=R/2` When joined across a voltage source in series heat PRODUCED in time t `H_s=V^2/R_p.t =(V^2t)/((2R))=(V^2t)/(2R)` and heat produced in parallel arrangement `H_p=V^2/R_p.t=(V^2t)/(R/2)=(2V^2t)/R` `therefore H_s/H_p= ((V^2t)/(2R))/((2V^2t)/R)=1/4 or H_s:H_p=1:4]`