Power transmission lines often use a form of electric current called alternating current, but in many regions, such as the Province of Quebec, high-voltage direct-current lines are used instead. Direct current is the kind of electric current you are studying in this chapter. A certain direct-current power transmission line has a resistance of 0.255 Ω/km. 812 kV of potential drives the current from the generating station to a city located 125 km from the plant. What is the power loss due to resistance in the line?
Rt = 0.255 Ohms/km * 125km = 31.875 Ohms. = Total rewsistance.
Pl = I^2 * Rt = I^2 * 31.875 = Pwer lost.
The power loss is proportional to the square of the current. Therefore, if we don't know how much current is flowing; we can't calculate the power loss.
To calculate the power loss due to resistance in the line, we can use the formula:
Power Loss = (Resistance per unit length) * (Length of the transmission line) * (Current)^2
Given data:
Resistance per unit length = 0.255 Ω/km
Length of the transmission line = 125 km
Potential difference (V) = 812 kV = 812,000 V
First, we need to calculate the current flowing through the transmission line using Ohm's law:
Current (I) = Voltage (V) / Resistance
Converting the voltage to volts (V):
Voltage (V) = 812,000 V
Converting the resistance to ohms (Ω):
Resistance (R) = 0.255 Ω/km * 125 km = 31.875 Ω
Current (I) = 812,000 V / 31.875 Ω = 25,440 A
Now, we can calculate the power loss:
Power Loss = (Resistance per unit length) * (Length of the transmission line) * (Current)^2
= 0.255 Ω/km * 125 km * (25,440 A)^2
Note: The power loss is usually given in watts (W). In this case, the unit will be (Ω/km * km * A^2), which simplifies to (Ω * A^2).
Calculating:
Power Loss = 0.255 Ω/km * 125 km * (25,440 A)^2
Therefore, the power loss due to resistance in the line is equal to the result obtained from the calculation above.