Answer:
We know that the resistance of a material is its length divided by its cross-sectional area and all that multiplied by its resistivity
Hence, resistance = ρ * length(in m) / Cross-sectional area
(ρ = constant of resistivity)
If you do not understand cross-sectional area, comment on this answer
since both the wires are made of the same substance, both their resistivity will be the same
since we are told that both the wires have the same resistance,
(ρ * length 1) / cross-sectional area 1 = (ρ * length 2) / cross-sectional area 2
since they both have the same resistivity, both the ρ will cancel out
length 1 / cross-sectional area 1 = length 2 / cross-sectional area 2------(1)
Calculating the cross-sectional area
To simplify it , the cross-sectional area is the area of the circle you can currently see on either of the wire
let the radius of wire 1 = 2r
then, the radius of wire 2 = r
Cross-sectional area 1 = π (2r)^2 = 4πr^2
Cross-sectional area 2 = π (r)^2
Now, using these values in (1)
l / 4πr^2 = l' / πr^2
l / l' = 4πr^2/πr^2
l / l' = 4 / 1
the length of rod 'P' is l
from the equation, we can simplify:
l (length of rod 'P') = 4 l'(length of rod 'Q')
Therefore, we can say that the length of rod 'P' is 4 times the length of rod 'Q'
