Two wires A and B are such that the radius of A is twice that of B and the length of B is twice that of A. If the two are of the same material, the ratio resistance of A /resistance of B would be 1/8
<h3>What is resistance?</h3>
Resistance is the obstruction of electrons in an electrically conducting material.
The mathematical relation for variation in resistance with length is given by
R = ρ*L/A
where r is resistance
ρ is the resistivity constant for
L is the length of the wire
A is an area of the cross-section for the wire
From the above relation that resistance is inversely proportional to the area of the wire keeping other parameters constant.
As given in the problem Two wires A and B are such that the radius of A is twice that of B and the length of B is twice that of A. If the two are of the same material (ρ)
Ra/Rb = (ρa*La/Aa)/ (ρb*Lb/Ab)
as given material of both the wire is same
ρa =ρb
As the given radius of A is twice that of B this means an area of A is four times that of B because Area = 2πr²
Aa = 4 Ab
The length of B is twice that of A
Lb = 2La
By substituting all the values in resistance formula
Ra/Rb = (ρa*La/Aa)/ (ρb*Lb/Ab)
Ra/Rb = (La/4Ab)/ (2La/Ab)
Ra/Rb = 1/8
Thus, the ratio resistance of A /resistance of B would be 1/8
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