Wires 1 and 2 are made of the same metal. wire 2 has twice the length and twice the diameter of wire 1. what are the ratios (a) ï2/ï1of the resistivities and (b) r2/r1of the resistances of the two wires?

(a) The resistivity of a substance is the resistance of a substance per unit length and per unit cross section at a given temperature. Since both wires are made of the same substance and I assume are at the same temperature, the ratio i2/i1 for those wires will be 1. (b) The resistance of a wire is described by the following equation R = pl/A where R = Resistance p = resistivity of material l = length A = cross sectional area Now the cross section of the wire is defined as pi*r^2 and r is one half of the diameter. So wire 2 will have a radius twice that of wire 1, so the cross section will differ by the square of the differences in the radius. So wire 2 will have a cross section 2^2 = 4 times that of wire 1. So the ratio r2/r1 = (p*2/4)/(p*1/1) = (2/4)(1/1) = 0.5/1 = 0.5 So wire 2 will have half the resistance of wire 1.