Question

Two metallic wires `A and B` (of the same material) are connected in parallel. Wire `A` has length `l` and radius `r` , wire `B` has a length `3 l` and radius `3 r`. Compute the ratio of the total resistance of parallel combination and the resistance of wire `A`.

Answer 1

`R_A = (rho l)/(pi r^2), R_B = (rho(3 l))/(pi (3 r)^(2)) = (1)/(3) ((rho l)/(pi r^2)) = (R_A)/(3)` Thus, `R_P = (R_A R_B)/(R_A + R_B) = (R_A (R_A//3))/((R_A + R_A //3)) = (1)/(4) R_A` or `(R_P)/(R_A) = (1)/(4)`.