Power Loss in a 10kV, 5ohm Transmission Line

PERE = POWER / VOLTAGEIn summary, to calculate the power loss in a transmission line with a resistance of 5 ohms when 10,000 kW are transmitted at 10 kV, use the formula P = VI = I^2R where V is the voltage drop, I is the current, and R is the resistance. The current can be found by dividing the power by the voltage using the formula I = P/V.
  • #1

DB

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-A transmission line has a resistance of 5 ohms. Calculate the power loss in the line when 10 000 kW are transmitted at 10 kV...

I don't know where to start, what formula am I supposed to use? I'm sure the second I find out its going to be soo easy, but any help would be apreciated.

Thanks in Advance
 
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  • #2
DB said:
-A transmission line has a resistance of 5 ohms. Calculate the power loss in the line when 10 000 kW are transmitted at 10 kV...

I don't know where to start, what formula am I supposed to use? I'm sure the second I find out its going to be soo easy, but any help would be apreciated.
Use:

[tex]P = VI = I^2R[/tex] where V is the voltage drop over the transmission line and I is the current it conducts, and R is the resistance of the line.
What is the current if the 10 kV line is conducting 10,000 kW (that is just P = VI)?

AM
 
  • #3


To calculate the power loss in a transmission line, we can use the formula P = I^2 * R, where P is the power loss, I is the current, and R is the resistance. In this case, we are given the voltage (10 kV) and power (10,000 kW), but we need to find the current in order to use the formula. We can use Ohm's Law, V = I * R, to solve for the current.

10 kV = I * 5 ohms
I = 10 kV / 5 ohms
I = 2000 A

Now, we can plug in the current into the power loss formula.

P = (2000 A)^2 * 5 ohms
P = 4,000,000 W or 4 MW

Therefore, the power loss in the transmission line is 4 MW. This means that 10,000 kW (or 10 MW) of power is being transmitted, but 4 MW is being lost due to the resistance in the line. This highlights the importance of minimizing resistance in transmission lines to reduce power loss and improve efficiency.
 

1. What is the cause of power loss in a 10kV, 5ohm transmission line?

The main cause of power loss in a transmission line is due to the resistance of the line itself. In this case, the 5ohm resistance of the line causes a portion of the power to be converted into heat, resulting in power loss.

2. How does the length of a transmission line affect power loss?

The longer the transmission line, the higher the resistance and therefore, the greater the power loss. This is because the electricity has to travel a longer distance and encounters more resistance along the way.

3. Can power loss be reduced in a 10kV, 5ohm transmission line?

Yes, there are several ways to reduce power loss in a transmission line. One method is by using thicker wires with lower resistance, which can decrease the overall resistance of the line. Another approach is to use superconducting materials, which have zero resistance and can significantly reduce power loss.

4. How does the frequency of the electricity affect power loss in a transmission line?

The higher the frequency of the electricity, the higher the power loss in a transmission line. This is because at higher frequencies, the electricity has a tendency to travel on the surface of the wire, increasing the resistance and resulting in more power loss.

5. Are there any external factors that can contribute to power loss in a 10kV, 5ohm transmission line?

Yes, there are external factors that can contribute to power loss in a transmission line. Weather conditions such as extreme heat or cold can affect the resistance of the wires and increase power loss. Additionally, poor maintenance or damage to the transmission line can also lead to higher power loss.

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