Question

a wire of resistance 12.8 ohm is cut into equal pieces and again joined in parallel and resistance is coming to 0.2 ohm. Find the number of pieces?​

Answer 1

say N is the number of parts, resistance of each part = 12.8/N (Resistance is proportional to length and inversely proportional to cross section and here cross section remains same ). Equivalent resistance ‘Req’ of N equal resistances of value 12.8/N connected in parallel

1/Req=1/(12.8/N) + 1/(12.8/N) + ……+1/(12.8/N) (Total N terms)

1/Req =N/(12.8/N)

or 1/Req = N^2/12.8

or Req=12.8/N^2

Req=0.2 ohm (given)

so N^2= 12.8/0.2 = 64

or N= +8 0r -8

As N can not be -Ve

N or number of parts= 8