Question

A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. The copper resistivity is 1.72 × 10⁻⁸ Ω.m.

a). What is the potential drop across the cable?

Answer 1

The potential drop across the copper transmission cable is 27,435.63 V.

Step-by-step explanation:

To calculate the potential drop across the copper transmission cable, we can use Ohm's law. Ohm's law states that the potential difference (V) across a conductor is equal to the product of the current (I) flowing through the conductor and the resistance (R) of the conductor: V = I * R.

First, we need to determine the resistance of the cable. The resistance of a conductor can be calculated using the formula: R = (resistivity * length) / (cross-sectional area). In this case, the length is 100 km (or 100,000 m) and the diameter is 10.0 cm (or 0.1 m). We need to convert the diameter to radius, so the radius is 0.05 m. The cross-sectional area of the cable is therefore given by: A = π * r^2 = π * (0.05)^2 = 0.00785 m^2. Plugging these values into the formula, we can calculate the resistance: R = (1.72 x 10^-8 * 100,000) / 0.00785 = 219.49 Ω.

Now we can use Ohm's law to calculate the potential drop: V = I * R = 125 * 219.49 = 27,435.63 V.