Question

Two wires A and B are of equal lengths,different are of cross-section and made up of same material

(i) Name of the property which is same for both the wires

(ii) Name the property which is different for both the wire

(iii) If the resistance of wire A is 4 times the resistance of wire B ,calculate

(A)the ratio of the area of the cross-section

(B)the ratio of the radii of the wires

Answer 1

(i) The resistivity of the two wires will be same.

(ii) The resistance of the two wires will be different.

(iii)

We know,

R = qL/A

So,

R_A/R_B = (L_A)(A_B)/[(L_B)(A_A)]

=> 4 = [A_B/A_A]

=> A_A/A_B = 1/4

=> Ratio of area of cross-section of wire A to area of cross-section of wire B is = 1 : 4

Again,

A = Ï€r²

So,

A_A/A_B = (r_a)²/(r_b)²

=> ¼ = (r_a)²/(r_b)²

=> r_a/r_b = ½

=> Ratio of radius of wire A to radius of wire B is = 1 : 2