the restivity of aluminium is twice that of copper and its density one third that of copper. the ratio of the Resistance of aluminium to copper wires having the same length and same mass per unit length is
Answers
The Resistivity of the wire will not change with the change in length. Resistivity is a property of the wire, it doesn't depend upon it’s length or cross-sectional area.
However, If you are asking about Resistance, it will increase to 4 times it’s initial value.
Resistance,R = ρl/A
Where,
ρ=Resistivity of the wire
l=lenght of wire
A= cross section of the wire
So, now if you increase the length of wire by 2 times it’s cross-sectional area will decrease by 2 times, because the volume of the wire has to remain constant.
Let, the initial and final radius of the wire be r1,&r2 respectively.
Since the initial and final volume are equal, so
2π(r1^2)l = 2π(r2^2)(2l)
So, r2=r1/√2
So, the cross-sectional area becomes 1/2 times the initial value.
Putting the values in the formula for resistance, we get the new resistance 4 times greater than the initial vakuev of resistance.