Two conducting wires of the same materialand of equal lengths and equal diameters 1 are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced inseries and parallel combinations would be-

Two conducting wires of the same materialand of equal lengths and equa

1.	Two conducting wires of the same materialand of equal lengths and equal diameters 1 are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced inseries and parallel combinations would be-
Answer» `1 :2` `2 : 1 ` `1 :4 ` `4:1` Solution :As both the wires are made of the same material and are of EQUAL lengths and equal diameters. they have the same resistance R. When they are CONNECTED in series their equilvalent resistance `R_s` would be - `R_s = R + R = 2R` and when they are connected inparallel their equivalent resistance `R_p`is given by `1/R_p = 1/R + 1/R =2/R` `:. R_p =R/2` Now. heat produced in time t is `H = (V^2t)/(R)`. As here source voltage V is same, when wires are conncted in series, `H_s = (V^2t)/(R_s) = (V^2t)/(2R)` When wires are connected in parallel, `H_p =(V^2t)/(R_p) =(V^2t)/(R/2) = (2V^2t)/R` `:.` The RATIO of heat produced, `H_s/H_p = (V^2t)/(2R) xx R/(2V^2t) = 1/4` `:. H_s : H_p= 1: 4`