 ###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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# Power

Jonathan Osbourne ###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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Power is the rate of energy use of electric circuit. The way that we calculate power is through the equation power = current x potential difference = (potential difference)^2/resistance = current^2 x resistance.

Alright so let's talk about power in electric circuits alright the idea is that in order for me to get current to flow through a resistor or really through any circuit at all I've got to give it some energy. I need energy to drive current through the circuit and that's actually the purpose of the battery. The battery is going to supply energy, now obviously if you got the circuit running for longer you're going to use more energy. So it's more useful for us to go to power which is rate of energy use, alright so let's start off with energy equals charge times potential difference and that's just basically the definition of potential difference. So but that's energy what about power? Well power is energy per unit time so when I divide by time I'm going to associate that division with the charge, so I'll get charge divided by time times potential difference. But charge divided by time is the current so that gives us the most basic and simple expression for power p equal iv current times potential difference.

This is often the one that you want to use if you're interested in how much power is being supplied to a circuit by a battery. So let's take an example 4 amps of current are running through a 12 volt battery so that 12 volt battery is pushing 4 amps of current and I want to know hw much power is delivered to the circuit by the battery. Well power equals iv so I got 4 times 12, 48 watts notice again we're doing everything in SI units and that means everything is in SI units. So if it's a power it's watts alright now most of the time when we're asking about power we're really thinking about resistors. So what we can do is we can re-write this standard formula using ohms law because current is v over r so that means that I can also write power as v squared over r. I also know that potential difference is current times resistance, so that means that I can also write it as i squared r. These are the 3 basic formulas that you'll see most often on introductory Physics tests and they're real, real easy to remember.

The first one power equals iv like a hospital, second one v squared over r you ought to recognize that formula from centripetal acceleration you're going in circle with radius r at speed v you require an acceleration v squared over r. Now this v of course is potential difference and this r is resistance. But it still sounds the same so it makes it easy to remember but this last one I didn't have a good way to remember this one until a student of mine about 6 years ago said that she'd heard somewhere twinkle, twinkle little star power equals i squared r which I just thought was great so those are real, real simple ways to remember these formulas which one do I use? Well that depends on which information I have. Most of the time I have the resistance so I don't want to use iv, okay because then I've go calculate something that they didn't even give me for free right? So I'd like to use this one if I know the potential difference and this one if I know the current.

Alright let's see how this goes, suppose that I've got a circuit like this one and I want to know how much power is used in this 2 ohm resistor right here alright really simple. This 2 ohm resistor is in parallel with the battery so that means the potential difference across it is 6 volts see? Potential difference is 6, resistance is 2 so what do we got? 6 squared over 2, v squared over r 18 watts alright. What about this 1 ohm resistor here alright this is a little bit more complicated because I don't know the potential difference across it so what I need to do because this 1 ohm is in series with the 2 ohm resistor is I need to calculate the current. Because current is the same in series alright so 6 volts dropped over a total of 3 ohms so that means the current is 2 amps alright now I know the current I know the resistance so I'm going to use my twinkle, twinkle little star. i squared r so it's 2 squared times 1 4 watts alright what about in this 2, well in this 2 it'll be same current so it'll be 2 squared times 2 so that's 8 watts in the other 2 ohm and if I add it all together I get 18 plus 4 plus 8 and that's 30 watts total that's being supplied. Alright now let's check that out, let's just check that out because it's always useful to go through all the Math and make sure that we're good alright. So I got 2 amps coming here how many amps do I have coming here? Well 6 divided by 2 is 3 so I got 3 amps in this arm, 2 amps in this arm so how many amps are going through the battery? 5 because we got to add them together so the 5 come in 3 go down over here and 2 go over here alright.

I've got a battery 6 volts current 5 amps so how much power is this batter giving the circuit? iv 5 times 6 is 30 watts in agreement with what we got down here for the total power that's used. It has to work that way power in equals power out alright. Now one other important thing to think about when you're thinking about power is that when you've got resistors connected in series the current is the same, so that means that I'm looking at i squared r. So that means the bigger the resistor the more power r big power big. So the smallest resistor in series will use the smallest amount of power alright. You might think why I'm I even saying that? In parallel it works a different way, in parallel it's the potential difference that's the same not the current. So in parallel I don't use i squared r because I don't know i I use v squared over r and that means that in parallel the smallest resistor uses the most power okay and that's counterintuitive but it's true. So resistance goes up power goes down the biggest resistor in a parallel combination uses the smallest amount of power and one real simple way to think is that you don't want to take a paper clip and stick it into an outlet. Why? Real small resistance on a parallel circuit equals huge amount of power and your circuit breaker's blow. Alright that's power.