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### Course: AP®︎/College Physics 2>Unit 3

Lesson 1: Current, resistivity, and Ohm's law

# Electric power

In this video David derives the formula to find the power used by a resistor. Created by David SantoPietro.

## Want to join the conversation?

• I got a general question about electric power:
At school, I have been told that the power loss in A.C transmission is minimized when voltage is maximized and current is minimized, but why is it so? Isn`t power proportional to both voltage and current? Please this is really worrying me. Thanks!
• Hello Karoomoogon124,

You are very close to the answer:

1) Power lines have resistance. There will be a power loss calculated as I^2R. By inspection, this loss can be reduced by either reducing the resistance or reducing the current. Reducing the resistance is not economical as more conductor would be required along with the added cost of supporting the transmission line...

2) There is a electrical component you need to understand. The backbone of our AC transmission system is the transformer. This allows us to step the voltage up or down as desired. A transformer is very efficient (high 90%). For our discussion let's assume the efficiency is 100%. Consequently power in equals power out.

3) Using a transformer let's take 100 V from our generator and use a transformer to step the voltage up by a factor of 10. Since our ideal transformer is 100% efficient the current has been reduced by a factor of 10. This must be so as P = IV.

4) We send the high voltage but low current through the transmission lines. At the other end we use a transformer to step the voltage back down.

Your teacher is correct a high voltage low current is the way to transmit electrical power. Since the resistance of the power line is fixed we get the greatest economy when the current is low and the voltage high. The transformer is the key to the entire process.

Keep going - there are many fascinating levels to this topic waiting for your discovery.

Regards,

APD
• This lesson quickly gets ahead of itself when done after the first few in "Ohm's law and circuits with resistors" He very quickly runs through definitions using symbols that haven't been explained yet...Or maybe I'm just stupid haha
• In a circuit, P = IV, where P is the power, I is the current, and V is the voltage. Depending on information you are given, you can sub in IR for V if needed.
• To make an electrical appliance work, why is it necessary that it gets x amount of energy per second(watts)? Would it still work if I were to give the same amount of energy over a longer period on time or a shorter period of time?
Thanks
• I'm pretty sure it is that dynamite has more power due to it (power) being the rate at which energy is released, while gasoline has more energy but less power - as it burns over a longer period of time.
(1 vote)
• Does more current mean faster moving electrons or is it more magnitude of electrons?? David mentions at that the electrons can't go faster because the current must be same
• More current can mean the the electrons are moving faster or that there are more electrons. Current is the amount of charge that passes a particular point in a given amount of time.
• Why does David show the positive charges to be flowing through the resistor? Don't the negative charges (electrons) flow from the negative terminal to the positive terminal but not the positive charges?

Thanks
xD
• Yes, the electrons are the particles moving to produce the current, however, this was not known at the time current was defined. It was thought that positive charges moved to create current, so the current direction is the opposite of the movement of the electrons. Since the definition of current had already become convention around the world, it was never corrected.
• It says that a resistor is measured by watts , like it says if , the power of a resistance is 20 watts , then it converts 20 joules of energy into something else in 1 sec.

Now my question is why is a resistor measured in watts and not in Ohms ?
• The resistance of the resistor is not measured in watts, it's measured in Ohms.
If you want to put a very high voltage, and therefore a lot of current, through a resistor, and you know it's going to get hot (because that's what resistors do, they dissipate energy), then you can imagine that you might need a different version of, say, a 10 ohm resistor to carry 10 amps than you would if you wanted it to carry 100 milliamperes. Therefore there are different power ratings of different resistors. "This is a 10 ohm resistor that can handle 100 Watts" is different from "this is a 10 ohm resistor that can handle half a watt". The first one will be big and fat. The second one will be much smaller.
• In the equation P=(I^2)R, power dissipated is directly proportional to the resistance of the resistor. But in the equation P=(V^2)/R, power dissipated is inversely proportional to the resistance of the resistor. This seems contradicting! How can this contradiction be solved?
• It's not contradictory because I and V are not independent.
When you say "is directly proportional to the resistance", that's true if you hold I constant, but not if you change I.
• Why is V2 - V1? Shouldnt it be V1 -V2 since U = Va - Vb? Does it matter?