E&M question: power lost in cables

[tamtam402]

Homework Statement

First of all, sorry for my bad english.

I have this problem and I've been trying to come up with something for 1h without success.

A circuit is "given" 100kW (100 000W)
The total resistance of the cables the electricity goes through is 5 ohms.
The voltage difference (deltaV) measured between the 2 extremities of the circuit is 10^4V.

I am asked to measure the lost power in the cables.

I know the answer, and it is 495Watts.

I have no idea how to do this, anyone care to help me out? Even with the answer, I can't come up with the solution.

Homework Equations

P=deltaV^2/R=VI
V=RI

The Attempt at a Solution

Well I tried everything I could. If I plug the given deltaV and given R in the P=deltaV^2/R equation, it gives me a power if like 20000000, which is even bigger than the power mentionned in the problem. I don't understand.

 

[tamtam402]

I just came up with something, but I don't get the same answer.

100 000/10^4=10A current
10A*5 ohms=50V
50V*10A=500W

How did they get 495W instead of 500W though?

 

[marcusl]

This doesn't make sense as written. Can you copy the problem for us verbatim?

 

[tamtam402]

This doesn't make sense as written. Can you copy the problem for us verbatim?

Unfortunately it's from a french book.

It says a power station gives 100kW of power to an electrical network. The resistance in the cables of said network is 5 ohms. After that, it is stated that the potential difference (deltaV) between both extremities of the network is 10^4 volts. I am asked to find the power lost in the cables.

I came up with this:
P=VI, so I=P/V=100000/10000=10A
V=RI, so V=5*10=50A

Using P=VI again, P=50*10=500W

The answer given by the book is 495W. What have I done wrong?

 

[rwisz]

Based on the given information, the power lost in the cables can be calculated using the equation P=I^2R, where I is the current flowing through the cables. To find the current, we can use Ohm's law, V=IR, where V is the voltage difference and R is the total resistance of the cables. So, the current can be calculated as I=V/R=10^4V/5ohms=2000A.

Now, using the equation P=I^2R, we can calculate the power lost in the cables as P=(2000A)^2*5ohms=4*10^6W=4MW. This value is much larger than the given power of 100kW. This is because the given power of 100kW is the power supplied to the circuit, not the power actually consumed by the circuit.

To find the actual power consumed by the circuit, we can use the equation P=VI, where V is the voltage difference and I is the current consumed by the circuit. Since the circuit is given 100kW, the power consumed by the circuit is also 100kW. So, we can calculate the current consumed by the circuit as I=P/V=100000W/10^4V=10A.

Now, using the equation P=I^2R, we can calculate the power lost in the cables as P=(10A)^2*5ohms=100W. This value is much closer to the given answer of 495W.

In conclusion, the power lost in the cables is 100W, not 495W. The given answer may be incorrect or there may be some other information missing in the problem. It is always important to double-check the given information and equations before attempting to solve a problem.