Question

Two conductors are made of the same material and have the same length. The conductor A is a solid wire 1 mm in diameter; conductor B is a hollow tube with an outside diameter of 2 mm and an internal diameter of 1 mm. What is the ratio between the resistances of the two wires, RA / RB? At resistances are measured between the ends of the wires.

Answer 1

reistance is given by,

R = *L/A

here, = resistivity of material

L = length of wire

A = cross section area of wire = pi*d^2/4

given, both wires are made of the same material and have the same length.

then, _A = _B

also, L_A = L_B

So, R_A/R_B = (d_Bo^2 - d_Bi^2)/(d_A^2)

given, d_Bo = outside diameter of conductor B = 2 mm

d_Bi = inside diameter of conductor B = 1 mm

d_A = diameter of conductor A = 1 mm

So, R_A/R_B = (2^2 - 1^2)/1^2 = 3/1

R_A/R_B = 3

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