The amount of heat energy transferred, each second, from the wire to the air = Power loss
Below is the math!
P = V * I
V = I * R
P = (I * R) * I
P = I^2 * R
This equation helps you determine the magnitude of the power loss.
The power loss = 625^2 * 5 = 1,953,125 watts = 1.953125 * 10^6 watts = 1.953125 MW
The maximum power loss in the cable = 1.953125 MW
I say maximum, because the amount of current flowing through the cable is determined by the customers! As people turn on their air conditioners, energy is required to operate the air conditioner. The electrons in the current carry the energy from the power station to the air conditioner. So, more energy means more current flowing through the cable. More current produces more heat energy in the aluminum wire in the cable.
Heat energy produced = Power loss * time
Power loss = 1.953125 * 10^6 watts
1 watt = 1 joule per second.
Heat energy produced = 1.953125 * 10^6 J/s * time
In 1 second, the heat energy produced = 1.953125 * 10^6 J/s * 1s = 1.953125 * 10^6 Joules of heat energy
So, each second, 1.953125 * 10^6 Joules of electric energy is converted into 1.953125 * 10^6 Joules of heat energy
The total power from the power station = 250 MW
The total power after the power loss = 250 – 1.953125 = 248.046875 MW
This is the power that is available for the customers to use.
What is the current in the power lines? 625 amps
What is the power loss in the cable? 1.953125 MW
P = I^2 * R
When people have less appliances turned on, less current is flowing through the long distance cables. If the current = 400 amps:
Power loss = 400^2 * 5 = 8 * 10^5 watts
This means the 8 * 10^5 Joules of heat energy was produced in the wire each second.