Answer :
If the total resistance is to be same, then the diameter of the new wire should be two times of the replaced wire.
The resistance of a wire is given by,
R = 4pL/πd²
Where,
R is the resistance,
p(rho) is the resistivity,
L is the length of the wire,
d is the are diameter of the wire.
The length of the replaced wire is four time of the previous wire and it is made up of same material. So, the resistivity will be same and it is said that the resistance has to be same,
So, we can write the new diameter d' in the relation as,
R = 4p4L/π(d')²
d'² = 4(4pL/πR
Putting, (4pL/πR) = d²,
d'² = 4d²
d' = 2d
The new diameter has to be two times of the previous diameter.
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