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. Find the ratio of heat produced in series and parallel combination.

Explanation

Suppose the resistance of each one of the two wires is R.
The equivalent resistance of the series combination,
`R_(1)= R+R= 2R`
The heat produced in time t,
`H_(1)= (V^(2))/(2R)t ( :. H= (V^(2))/(R)t)`…(1)
The equivalent resistance of the parallel combination is
`R_(P)= (R xx R)/(R+R)= (R^(2))/(2R)= (R)/(2)`
Heat produced in time t,
`H_(2)= (V^(2))/(R//2)t= (2V^(2)t)/(R)` ...(2)
From (1) and (2), we have
`(H_(1))/(H_(2))= (V^(2)t)/(R) xx (R)/ (2V^(2)t)`
`implies (H_(1))/(H_(2))= (1)/(4)`
`H_(1): H_(2)= 1:4`