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