Two conducting wires of the same material and 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 in series and parallel combinations would be-

Options

A. `1 :2`
B. `2 : 1 `
C. `1 :4 `
D. `4:1`

Answer

C

Explanation

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 in parallel 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`