Answer:
The resistance of the wire after it is stretched is 93.31R.
Explanation:
Resistance is the property of the material to oppose the current flow through it. It is given by the relation :
R = (ρl)/A
Here ρ is resistivity, l is length of wire and A is the area of the wire.
Let l₀, and A₀ are the original length and original circular cross section area of the wire. while l₁ and A₁ are the new length and new circular cross section area of the wire.
Volume of the original wire, V₀ = A₀ x l₀
Volume of the new wire, V₁ = A₁ x l₁
According to the problem. volume remain same. So,
V₀ = V₁
A₀ x l₀ = A₁ x l₁
It is given that l₁ = 9.66 x l₀. Substitute this value in the above equation;
A₀ x l₀ = A₁ x 9.66 x l₀
A₁ = A₀/9.66
Resistance of the original wire, R = (ρl₀)/A₀
Resistance of the new wire, R₁ = (ρl₁)/A₁
Substitute the value of l₁ and A₁ in the above equation.
R₁ = (ρ x l₀ x 9.66)/(A₀/9.66) = 93.31 x (ρl₀)/A₀
But (ρl₀)/A₀ = R. hence,
R₁ = 93.31 R
