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

(c) The Joule heating
is given by, *H = i*^{2}*Rt*

Let, *R* be the
resistance of the two wires.

The equivalent
resistance of the series connection is *R*_{S}*
= 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 *R*_{P}*
=
*

*V* is the applied
potential difference across this *R*_{P}*.*

The heat dissipated in
time *t* is,

So, the ratio of heat produced is,

Note: *H
R* also *H
i*^{2} 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 = i*^{2}*Rt*
to find the ratio.

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