Question

Determine the resistance of 3km of copper having a diameter of 0,65mm if the resistivity of copper is 1,7x10^8

Answer 1

Resistance of copper = 1.54 * 10^18 Ohms

Step-by-step explanation:

Given the following data;

Length of copper, L = 3 kilometers to meters = 3 * 1000 = 3000 m

Resistivity, P = 1.7 * 10^8 Ωm

Diameter = 0.65 millimeters to meters = 0.65/1000 = 0.00065 m

`Radius, r = \frac {diameter}{2}`

`Radius = \frac {0.00065}{2}`

Radius = 0.000325 m

To find the resistance;

Mathematically, resistance is given by the formula;

`Resistance = P \frac {L}{A}`

Where;

• P is the resistivity of the material.
• L is the length of the material.
• A is the cross-sectional area of the material.

First of all, we would find the cross-sectional area of copper.

Area of circle = πr²

Substituting into the equation, we have;

Area = 3.142 * (0.000325)²

Area = 3.142 * 1.05625 × 10^-7

Area = 3.32 × 10^-7 m²

Now, to find the resistance of copper;

`Resistance = 1.7 * 10^(8) \frac {3000}{3.32 * 10^(-7)}`

`Resistance = 1.7 * 10^(8) * 903614.46`

Resistance = 1.54 * 10^18 Ohms