Compute the resistance of a hardened copper rod 2 meters long and 8 mm in diameter if resistivity of the material is 1.756 x 10^ (-8) ohm-meters?

The resistance of the copper rod = 4.39*10⁻¹⁵ Ohms.

Explanation:

Resistance: This is the opposition to current flow in a circuit.

The S. I unit of resistance is Ohms.

R = Aσ/L ... Equation 1

Where σ = resistivity of the copper, R = resistance of the copper rod, A = cross sectional area of the copper, L = length of the copper rod.

Given:

σ = 1.756*10⁻⁸ ohm-meters, L = 2 meters.

But A = πd²/4

Where d = 8 mm = (8/1000) m = 0.0008 m, π = constant = 3.143

Therefore,

A = 3.143 (0.0008) ²/4

A = 0.0000005 m²

Substituting these values into equation 1,

R = 5*10⁻⁷*1.756*10⁻⁸/2

R = (8.78 * 10⁻¹⁵) / 2

R = 4.39*10⁻¹⁵ Ohms.

Thus the resistance of the copper rod = 4.39*10⁻¹⁵ Ohms.