Question

If two conducting wires of the same material and of equal length and equal diemeters and first connected in series and then in parallel in a circuit across the same potential difference then what would be the ratio of heat produced in series and in parallel combination.

Answer 1

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, Rs = R + R = 2R

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

Or, Rp = R/2

Now, heat, q = Ix t

Or, q = V2/R x t

So, qs = V2/Rs x t

And, q
= V2/R
x t

So, qs/q
= (V2/Rs x t)/(V2/R
x t)

= R
/Rs

= (R/2)/2R

= 1/4 or 1:4

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