Answer:
523.79 S/m
Step-by-step explanation:
To find the electrical conductivity (σ) of the material, we can use the formula that relates resistance, length, cross-sectional area, and conductivity for a cylindrical wire:
Resistance (R) = (ρ * L) / A
Where:
R is the resistance (given as 6 ohms).
ρ (rho) is the electrical resistivity of the material.
L is the length of the wire.
A is the cross-sectional area of the wire.
We are given the diameter of the ring, which is 5 cm. First, let's calculate the radius of the ring in meters:
Radius (r) = 2 mm = 0.002 meters (since 1 mm = 0.001 meters)
Now, let's calculate the cross-sectional area (A) of the wire:
A = π * r^2
A = π * (0.002 m)^2
A = π * 4e-6 square meters
Now, we need to find the length (L) of the wire. Since the wire forms a ring, the length is equal to the circumference of the ring. The circumference (C) of the ring can be calculated using the formula:
C = 2πr
C = 2π * 0.002 m
C = 0.004π meters
So, the length of the wire is 0.004π meters.
Now, we can plug these values into the resistance formula:
6 ohms = (ρ * 0.004π m) / (π * 4e-6 square meters)
Now, solve for ρ:
ρ = (6 ohms * 4e-6 square meters) / (0.004π m)
ρ = (24e-6 square meters) / (0.004π m)
ρ ≈ 1.909e-3 ohm·meters
So, the electrical conductivity (σ) of the material is the reciprocal of the resistivity:
σ = 1 / ρ
σ ≈ 1 / 1.909e-3 ohm·meters
σ ≈ 523.79 S/m (Siemens per meter)
The electrical conductivity of the material is approximately 523.79 S/m.