Question

A transmission-line cable with a length of 2 km consists of 19 strands of identical copper conductors, each 1.5 mm in diameter. Because of the twist of the strands, the actual length of each conductor is increased by 5%. Determine the resistance of the cable if the resistivity of copper is 1.72 µ?

Answer 1

To find the resistance of the transmission-line cable, you need to calculate the cross-sectional area of a single conductor and then multiply it by the number of strands. By substituting the given values into the formulas, you can find the resistance of the cable.

Step-by-step explanation:

The resistance of the transmission-line cable can be calculated using the formula:

R = (ρL) / (A)

Where:

• R is the resistance
• ρ is the resistivity of copper
• L is the length of the cable
• A is the cross-sectional area of the cable

To find the resistance, we need to calculate the cross-sectional area of a single conductor first:

A = πr2

Where:

• A is the cross-sectional area
• π is the value of pi (~3.14)
• r is the radius of the conductor

After calculating the cross-sectional area of a single conductor, we can find the resistance of the cable by multiplying the resistance of a single conductor by the number of strands:

Resistance of cable = Number of strands x Resistance of a single conductor

Substituting the given values into the formulas, we get:

• Aconductor = π(d/2)2
• Acable = Number of strands x Aconductor
• Rcable = (ρ x L x (1 + 0.05)) / Acable

Simplifying the equations, we find the resistance of the cable.