Question

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?

Answer 1

Answer:

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.