Question

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combination would be:
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1

Answer 1

assume the heat produced is measured for both in the same te interval

Answer 2

Answer:

1:4

Explanation:

Suppose the resistance of each one of the two wires is R.

The equivalent resistance of the series combination,

Rs = R + R = 2R

The heat produced in time to,

H1 = ( V^2 / 2R ) t ........…..…(1)

The equivalent resistance of the parallel combination I

Rp = ( R×R / R+R )

= R^2 / 2R = R/2

Heat produced in time to,

H2 = [V^2 / (R/2)] t

= 2V^2t / R ....................(2)

From (1) and (2)

H1 / H2 = V^2t / 2R × R / 2V^2t

= 1/4

H1 : H2 = 1 : 4