Question

1. Two conducting wires of the same material and equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference . What is the ratio of heat produce in series and parallel combinations?

Answer 1

Each point: 1 Mark

Since both wires are made of the same material and have equal lengths and equal diameters, these have the resistance. Let it be R

When connected in series, their equivalent resistance is given by

Rs=R+R=2R

When connected in parallel, their equivalent resistance is given by or 1Rp=(1R)+(1R)=2R⟹Rp=R2

Further, electrical power is given by P=V2R

Power (or heat produced) in series, Ps=V2Rp

Thus, PsPv=V2RsV2Rv=RvRs=R22R=14

or Ps:Pp::1:4