If a 483 kV transmission line is going to carry 1078 MW, what should be the characteristic impedance of the line to maintain a flat voltage profile? Choose the closest answer.
Question
If a 483 kV transmission line is going to carry 1078 MW, what should be the characteristic impedance of the line to maintain a flat voltage profile? Choose the closest answer.
Solution
The characteristic impedance (Z) of a transmission line for a flat voltage profile can be calculated using the formula:
Z = V^2 / P
where V is the voltage and P is the power.
First, we need to convert the voltage and power to the same units. In this case, we'll convert kilovolts (kV) to volts (V) and megawatts (MW) to watts (W).
1 kV = 1000 V 1 MW = 1,000,000 W
So, 483 kV = 483,000 V and 1078 MW = 1,078,000,000 W
Now we can substitute these values into the formula:
Z = (483,000)^2 / 1,078,000,000 Z = 233,289,000,000 / 1,078,000,000 Z = 216.5 ohms
So, the characteristic impedance of the line should be approximately 216.5 ohms to maintain a flat voltage profile.
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