Answer:
Length of the tungsten = 1636.4 m
Explanation:
Let's first find the cross sectional area of the wire:
Area = [tex]pi*D^2/4[/tex]
Area = [tex]3.1415*(0.191*10^-^3)^2/4[/tex]
Area = [tex]2.865*10^-^8[/tex] m^2
We can solve for the length using the equation of resistance:
Resistance = Resistivity * Length / Area
[tex]3210=(5.62*10^-^8)*Length/(2.865*10^-^8)[/tex]
Length = 1636.4 m
Answer:
1636 m
Explanation:
The formula for the resistance of a wire is given as,
R = ρL/A........................... Equation 1
Where R = Resistance of the wire, ρ = Resistivity of the wire, L = Length of the wire, A = cross sectional area of the wire.
But,
A = πd²/4.................. Equation 2
Where d = diameter of the tungsten wire
Substitute equation 2 into equation 1
R = 4ρL/πd²................ Equation 3
make L the subject of the equation
L = Rπd²/4ρ.............. Equation 4
Given: d = 0.191×10⁻³ m, ρ = 5.62×10⁻⁸ Ω m, R = 3210 Ω
Substitute into equation 4
L = 3210(3.14)(0.000191)²/(4×5.62×10⁻⁸)
L = (3.677×10⁻⁴)/(22.48×10⁻⁸)
L = 0.1636×10⁴ m
L = 1636 m
