Question

Two exactly similar heating resistances are connected (i) in series, and (ii) in parallel, in two different circuits, one by one. If the same current is passed through both the combinations, is more heat obtained per minute when they are connected in series or when they are connected in parallel? Give reason for your answer.

Answer 1

Let the resistance be R.
In a series combination:

Net resistance = R + R = 2R

In a parallel combination:

$\frac{1}{\mathrm{Net}\mathrm{resistance}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}$

Net resistance = $\frac{R}{2}$

It is clear that the net resistance is more in the series combination. Therefore, more heat will be obtained in a series connection, as the heat produced is directly proportional to the resistance in the circuit.