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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. The ratio of heat produced in series and parallel combinations would be −
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1
Asked by Pavithra Last Modified
Answer 
Vishaka Bhutia
Home Tutor
(c) The Joule heating is given by, H = i2Rt
Let, R be the resistance of the two wires.
The equivalent resistance of the series connection is RS = R + R = 2R
If V is the applied potential difference, then it is the voltage across the equivalent resistance.
The heat dissipated in time t is,
The equivalent resistance of the parallel connection is RP = 
V is the applied potential difference across this RP.
The heat dissipated in time t is,
So, the ratio of heat produced is,
Note: H 
R also H i2 and H t. In this question, t is same for both the circuit. But the current through the equivalent resistance of both the circuit is different. We could have solved the question directly using H R if in case the current was also same. As we know the voltage and resistance of the circuits, we have calculated i in terms of voltage and resistance and used in the equation H = i2Rtto find the ratio.
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