Two copper wires A and B of length 30 m and 10 m have radii `2 cm and 1 cm` respectively. Compare the resistances of the two wires. Which will have less resistance ?

Explanation

Let the two resistances be labelled as `R_1 and R_2`
Here, `l_1 = 30 m, A_1 = pi r_1^2 = pi (2 xx 10^-3) m^2`
As `R = (rho l)/(A), R_1 = (rho l_1)/(A_1)` and `R_2 = (rho l_2)/(A_2)`
Thus, `(R_1)/(R_2) = (rho l_1//A_1)/(rho l_2//A_2) = (l_1 A_2)/(l_2 A_1) = (30 xx pi(1 xx 10^-3)^2)/(10 xx pi(2 xx 10^-3)^2) = (3)/(4)`
Clearly, `R_1 lt R_2`.