Question

Two conducting wires of the same material and 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 1

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 ---heat in series connection

And, qp = V²/R_p x t -----heat in parallel connection

So,

= (R/2)/2R

= 1/4 or 1:4

Therefore option C is the answer.