Two wires of same length and area, made of two materials of resistiveity P1and P2are connected in parallel to a source of potential. The equivalent resistivity for the same length and area isρ1ρ2/(ρ1+ρ2).
But if the same wires are in series, then;
ρs2l/A= (ρ1+ρ2) l/A
Thereforeρs= (ρ1+ρ2)/2 [Since in series the length is doubled]
Similarly, shouldn't the area of cross section of the wires when placed in parallel too be doubled? On doubling the area;
ρ3 l/2A = {ρ1ρ2 *l/A/(ρ1+ρ2)}
Thereforeρ3 = 2ρ1ρ2/ (ρ1+ρ2)
But this is not so. Could you please explain in detail the contradiction?
the question is that equivalent resistivity with same length and area
so in series
ρequl/A= (ρ1+ρ2) l/A
ρequ= (ρ1+ρ2)
in parallel
ρequ=ρ1ρ2/(ρ1+ρ2).