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Question:

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

Answer:

The two conducting wires are of same material, same lengths and diameters. Therefore, their resistances are also expected to be equal.

Let the resistance in the wire to be R.

So in series, R_s = R + R = 2R

In parallel, 1/R_p = 1/R + 1/R = 2/R

Or, R_p= R/2

Now, heat, q = Ix t

Or, q = V²/R x t

So, q_s = V²/R_s x t

And, qp = V²/R_p x t

So, q_s/qp = (V²/R_s x t)/(V²/R_p x t)

= R_p/R_s