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A metal ring of diameter 5 cm and the radius of the wire was 2 mm is made of certain material of resistance 6 ohms find the electrical conductivity of its material

A metal ring of diameter 5 cm and the radius of the wire was 2 mm is made of certain-example-1

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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.

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