A high-voltage transmission line with a resistance of 0.28 /km carries a current of 1030 A. The line is at a potential of 720 kV at the power station and carries the current to a city located 165 km from the station.
(a) What is the power loss due to resistance in the line?
____________ W
(b) What fraction of the transmitted power does this loss represent?
____________%
R=.28*165 (calc this) plug into following equation and that will give you W
=I^2*R
=1030^2*R
b. P(loss)= IV
=1030(720000) <---changed into V from kv
=741400000
divide answer from part a by this number to get the percentage
To calculate the power loss due to resistance in the transmission line, we can use the formula:
Power loss = (Resistance per unit length) x (Length of the transmission line) x (Square of the current)
Let's calculate it step by step:
(a) Calculate the power loss due to resistance:
- Resistance per unit length: 0.28 Ω/km
- Length of the transmission line: 165 km
- Current: 1030 A
Power loss = (0.28 Ω/km) x (165 km) x (1030 A)^2
To find the answer, you need to square the value of 1030 A, then multiply it by (0.28 Ω/km) and (165 km).
(b) To calculate the fraction of the transmitted power that this loss represents, we need to use the formula:
Fraction = (Power loss) / (Transmitted power) x 100
The transmitted power can be calculated using the formula:
Transmitted power = Voltage x Current
- Voltage: 720 kV
- Current: 1030 A
Transmitted power = (720 kV) x (1030 A)
Once you calculate the power loss and the transmitted power, divide the power loss by the transmitted power, then multiply by 100 to convert it to a percentage.
Now, you can use these formulas and the given values to find the answers to both (a) and (b).