Two cylindrical conductors, one of copper and other of aluminium have the samelength and the same resistance. Resistivity of aluminium = 1.5 × resistivity of copper.Density of aluminium =31× density of copper. How many times is copper conductorheavier than aluminium ?

To solve this problem, we need to understand a few basic principles:

1. The resistance (R) of a wire is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.

2. The mass (m) of a wire is given by the formula m = ρV, where ρ is the density and V is the volume.

3. The volume (V) of a cylinder is given by the formula V = AL, where A is the cross-sectional area and L is the length.

Given that the two conductors have the same length and the same resistance, we can set up the following equations:

For copper: Rc = ρcL/Ac and mc = ρc'AcL For aluminium: Ra = ρaL/Aa and ma = ρa' AaL

Where ρc and ρa are the resistivities of copper and aluminium respectively, ρc' and ρa' are the densities of copper and aluminium respectively, and Ac and Aa are the cross-sectional areas of the copper and aluminium conductors respectively.

Given that Ra = Rc and ρa = 1.5ρc, we can equate the two resistance equations to get Ac/Aa = 1.5.

Given that ρa' = 3/10 ρc', we can substitute this and the previous result into the mass equations to get mc/ma = (ρc'AcL) / (ρa'AaL) = (ρc'/ρa') * (Ac/Aa) = (10/3) * 1.5 = 5.

Therefore, the copper conductor is 5 times heavier than the aluminium conductor.