Question

A transmission line that has a resistance per unit length of 4.50x10⁻⁴ Ω/m is to be used to transmit 5.00 MW across 400 mi (6.44x105 m). The output voltage of the source is 4.50 kV. (a) What is the line loss if a transformer is used to step up the voltage to 500 kV?

Answer 1

The line loss when a transformer is used to step up the voltage to 500 kV is 381 W.

Step-by-step explanation:

To calculate the line loss, we can use the formula P = I²R, where P is the power loss, I is the current, and R is the resistance per unit length. Since the voltage is stepped up to 500 kV, we need to find the current at the higher voltage first. We can use the formula P = IV to find the current, where P is the power and V is the voltage. Substituting the given values, we get:

Power = 5.00 MW = 5.00 × 10⁶ W
Voltage = 4.50 kV = 4.50 × 10³ V

From P = IV, we can rearrange the formula to get:

I = Power / Voltage = (5.00 × 10⁶ W) / (4.50 × 10³ V) = 1111.11 A

Now that we have the current at the higher voltage, we can calculate the line loss at the lower voltage using the formula P = I²R. Substituting the given values, we get:

Power Loss = (1111.11 A)² × (4.50 × 10⁻⁴ Ω/m) × (6.44 × 10⁵ m) = 3.81 × 10² W

Therefore, the line loss is 3.81 × 10² W or 381 W.

Answer 2

To find the line loss, we can use the power loss formula and substitute the given values. The line loss is 69 MW.

Step-by-step explanation:

To calculate the line loss, we need to find the power loss in the transmission line. The power loss can be calculated using the formula:

Power Loss = (Resistance per unit length) x (length) x (current)^2

Given resistance per unit length = 4.50x10⁻⁴ Ω/m, length = 6.44x10^5 m, and current = (output voltage)/(line voltage) x (power to be transmitted), we can substitute these values into the formula to find the line loss. In this case, the line voltage is 500 kV because it is stepped up from 4.50 kV. The power to be transmitted is 5.00 MW.

After calculating, we find that the line loss is 69 MW.