Hey physicists, this is Mr. Abramovich. We're going to talk about electrical power today. So what is power? You might remember this word from our unit on energy. Power is essentially the rate at which energy is used or transferred, or you could consider it to be the rate at which work is done because work is essentially the transfer of energy.
One example of where power would come into play is if you talk about... Walking up a set of stairs versus running up a set of stairs, you might be gaining the same amount of gravitational potential energy through the work you did, but by running, it's a higher power application because you picked up that potential energy more quickly. Another example is putting two equal-sized pots of water on the stove to boil.
One pot starts to boil sooner than the other. Even though you put the same amount of thermal energy into each pot, the one that boiled quicker had a higher power. Another example, if you think about the horsepower rating of engines, higher horsepower engines can turn the chemical energy in gasoline into kinetic energy more quickly than a lower horsepower engine. So the advantage of having a higher horsepower engine is that you can accelerate more essentially.
But electrical power is a thing too. Same deal for electrical applications as mechanical applications. We're talking about...
what can convert electrical energy into another form of energy more quickly. So we typically use watts for electrical devices. You'll see them on light bulbs.
You'll see them on appliances. You'll have a higher power appliance when you need to access a lot of energy fast, when you need to do that work quickly. So things like hair dryers, blenders, vacuum cleaners, they're converting that energy fast to have a quick burst of energy. So they're going to... have higher power ratings.
The downside of that means that if you leave the device on, it's going to go through more energy over the course of the day because it's converting the energy at a faster rate. That's what's going to cost you more on your electric bill. So if you have the option of having an old school incandescent light bulb, it's maybe 60 watts or an LED light that might be six watts. It's going to be a 10th of the energy consumption when left on over the course of the day.
the course of the day it'll be a tenth as expensive as it would be to have a 60 watt light bulb to have an led so how do we measure power well power is measured in watts and a watt is a joule per second the rate at which the joules are transferred where j is the joule s is a second so if power shows you how fast energy is transferred or used and voltage describes the amount of energy you that each charge going through your circuit carries, and current describes how fast the unit of charge is moving through the circuit. Well, what if we put those quantities together? You have voltage, which is the amount of energy in each unit of charge, the current, which is the rate at which the charges are moving through.
If you multiply those together, you're left with the energy transfer in a given amount of time. So voltage times current. will give you power. And a watt is actually a volt times an amp because a volt is a joule per coulomb.
An amp is a coulomb per second. So when you multiply them together, you're left with joules per second. This should make sense because if I asked you what makes a light bulb bright, some people would say more voltage.
Some people would say more current, but it's really both. It's the product of both of those quantities that give you the brightness of a light bulb. because the higher power light bulbs are going to be piling on that light energy in less time. You're going to get more brightness out.
So there's actually three convenient ways we can find power directly from what we know. We can use that equation we looked at on the last slide, where you just take the current and the voltage and multiply them to get power. But if we don't have current or voltage handy, we can use identities from Ohm's law for both of those quantities and make a substitution.
Like, say... we don't know the current but we know the resistance, we could do voltage over resistance in place of current and use v squared over r to get power. Or if we don't know the voltage, substitute in i times r for voltage and that'll give us i squared r for a different power formula.
So that's just another way you could calculate power based on what you already know. So for example, say you plug in a 60 watt light bulb into a 120 volt outlet. And that's generally what all outlets are in your house except for the 240 ones that you might plug a washer or dryer into. How much current will that light bulb draw? So it's important to know that the power rating of a light bulb, in this case, a 60-watt light bulb, goes along with a particular voltage.
The 60 watts means that it'll be a 60-watt light bulb when you plug it into a 120-volt outlet. If you put a 60-watt bulb into some other voltage source, you might not get 60 watts out of it. So to solve this problem, if we want to find how much current it draws, we just rearrange the equation and isolate current. We can plug in 60 watts for the power, 120 volts for the voltage, and you'll get a half amp out of it.
A spin on this problem would be, what if we want to, oh, by the way, it's handy to know that how much current your appliances are drawing based on their power rating and the voltage you're plugging them into. Because if you run multiple devices at the same time and you pull out too much current, you might trip the circuit breaker, which has happened to me at my house when... I turn on the blender to make breakfast while my girlfriend's in the other room drying her hair and then the power goes out. So it's helpful to know how much current you're going to be using at one time. A spin on this problem would be if you plug a 60 watt light bulb into a 120 volt outlet.
How much resistance does the bulb have in this case? Well you could use the other version of the equation, B squared over R and plug in 120 volts to 60 watts and you'll get 240 ohms for a light bulb resistance. All right, so if you've ever seen the electric meter outside of where you live, you'll see that there's a unit of kilowatt hours. Kilowatt hours is actually a unit of energy. It's not as clean looking as a joule.
But if you think about it, kW is kilowatts, h is hours. If power is energy over time, you can isolate energy by multiplying power times time. So even if the kilowatts and the hours don't cancel nice and clean, by multiplying and you're still getting an energy unit.
If you look at your electric bill, this is just a sample electric bill, you're going to get charged a dollar rate for the kilowatt hours of energy that you use. Multiply the rate by the kilowatt hours on your meter reading, you'll get the total cost. So here, if someone consumed 575 kilowatt hours in a month, and you're charged at a rate of...
$0.03 per kilowatt hour, it's going to be a $16 bill at the end of the month. Why don't they just charge you for the joules? Why use kilowatt hours? Well, joules are tiny. And the amount of energy you're using over a month is going to be a big amount of joules.
So it's more convenient to have it in terms of kilowatt hours. So say you're charged $0.12 a day per kilowatt hour. How much would it cost you to leave on a 1,440-watt air conditioner all day? Well, We'll figure out the kilowatts. One kilowatt for every 1,000 watts.
That's 1.44 kilowatts, the rate at which you're transferring the electrical energy into the energy you're getting out of the air conditioner. Next step, we're going to figure out the hours. So 24 hours in a day, no problem.
So we put our 1.44 kilowatts times 24 hours. That's 34.6 kilowatt hours. that you're using over the course of that day.
At the rate of 12 cents a kilowatt hour, that AC is costing you about $4 a day. You might say, okay, not so much. Over the course of a month, that ends up turning into 125 bucks to run your AC all day. So just keep in mind when you keep those appliances on, it is costing you something. There are ways you can save some money.
by keeping your place more energy efficient in the winter. I mean, you might not be paying your electric bills right now, but you will someday. So think about things like keeping your blinds closed at night to hold in more heat or checking seals on the windows to make sure that, that should say heat doesn't leak out, but I had heat doesn't leak in. That's a mistake. And there's also a service called MassSave that can help make your house more energy efficient and give you discounts on insulation, energy efficient light bulbs, power strips, that kind of thing to help you save some money on your electric bill.
So you're not consuming as much. So that's all I got. Hope this was helpful. And ask your physics teacher if you have a question.