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
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
Ans (c) 1:4
(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 α R also H α i2 and H
α 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
α 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
= i2Rt to find the ratio.
