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 21 and radius 2r. Calculate the ratio of the equivalent resistance in parallel combination and the resistance of wire A.

Answer 1

Resistance of A = l/πr^2
Resistance of B = 2l/π(2r)^2
= 2l/4πr^2
Resistance in parallel
1/R = 1/(l/πr^2) + 1/(2l/4πr^2)
1/R = πr^2/l + 4πr^2/2l
1/R = πr^2/l + 2πr^2/l
1/R = 3πr^2/l
R = l/3πr^2

Resistance A : Parallel combination resistance
= l/πr^2 ÷ l/3πr^2
= l/πr^2 x 3πr^2/l
= 3/1
So the ratio is 3 : 1 .

Answer 2

may be the answer if any mistakes plzz tell and thanks for the question.