the resistance of 100.0cm of constantan wire whose diameter of cross-section is 0.55m is 5ohm
find the resistivity of constantan wire
resistance=resitivity(length/area)
solve for resistivity. Normally, One does not deal with wire that is that size. 55 cm diameter wire must be pretty heavy, at least one meter of it. I know my hoist could not lift it. It is bigger than the engine in my car.
To find the resistivity of the constantan wire, we can use the formula:
R = (ρ * L) / A
Where:
R is the resistance of the wire,
ρ (rho) is the resistivity of the material,
L is the length of the wire, and
A is the cross-sectional area of the wire.
Given:
R = 5 Ω
L = 100.0 cm = 1.0 m
d (diameter) = 0.55 mm
First, we need to calculate the cross-sectional area (A) using the formula:
A = π * (d / 2)^2
The diameter is given as 0.55 mm, so we need to convert it to meters by dividing it by 1000:
d = 0.55 mm / 1000 = 0.00055 m
Now, substitute the values into the formula:
A = π * (0.00055 / 2)^2
Calculating the right side of the equation, we get:
A = π * (0.000275)^2
A ≈ 2.3799563 x 10^-7 m^2
Now, rearrange the formula to solve for ρ:
ρ = (R * A) / L
Substitute the known values:
ρ = (5 * (2.3799563 x 10^-7)) / 1.0
Calculating the right side of the equation, we get:
ρ = 1.18997815 x 10^-6 Ω·m
Therefore, the resistivity of the constantan wire is approximately 1.18997815 x 10^-6 Ω·m.