# Power: Equations and Example

by Jared Rovny

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00:01 So a few things about power.

00:03 So we've said that power is the amount of work per unit time and has units of energy per unit time, and we've also said that power is a force times a velocity because we did a quick derivation to see that that is an equivalent expression.

00:15 And we can rearrange this upper equation, so this first top equation I've written, power is work per unit time, we can multiply both sides by time and see that I can find the amount of work done or the energy just by taking whatever power in watts and multiplying by the time.

00:31 By doing this, we can get one more time units of energy out of power times time, and so we'll still have joules.

00:38 Let's take a quick example because, in fact, this is something that you might be more familiar with than you realize.

00:44 If you have a light bulb, we often measure light bulbs in terms of watts.

00:48 We have a 10 watt or 20 watt, a 40 watt and a 60 watt, a 100 watt light bulb, and these watts are the units of power.

00:55 So it's telling you how much power your light bulb is using, or anything with watts is telling you how much power that object is using.

01:02 So, if we have say a 60 watt light bulb, what that's telling me is the light bulb is using 60 joules per second of energy because power is measured how much energy per unit time is being used by the light bulb.

01:16 So for example, if you wanted to know how much energy a light bulb that was 60 watts used in a course of 20 seconds, we could, according to the last equation here, multiply the power, the 60 watts or joules per second times the time, so say it was on for 20 seconds, then you would have 60 times 20 or 1200 joules that your light bulb used by being on for 20 seconds.

01:39 You also might remember or have seen this or heard this before, that when you're getting your energy bill or thinking about the amount of energy used, it's measured in kilowatt hours, and this is the exact same thing.

01:52 It looks a little bit different, instead of watts we now have kilowatts and instead of time just being in seconds we have it in hours and the only reason for that is because kilowatts and hours are better units for human applications and you're gonna pay out money based on how much energy you used, and that's why we have the units we have, kilowatts and hours.

02:11 By multiplying power which is in joules per unit time by time, we end up with units of energy, and that's what you're paying for is energy, the watts times the hours.

02:21 We can figure out how much energy in joules a kilowatt is very quickly, so a kilowatt is 1000 watts, we have 1 hour which is 3600 seconds, 60 minutes and 60 seconds together makes 3.600.

02:34 We multiply these together and we get a number in scientific notation of 3.6 times 10 to the 6th joules.

02:41 So, a kilowatt hour is a little over 3 million joules of energy that you're using and that's what you're paying for again, is energy, this quantity as you use appliances like light bulbs in your house or other places.

02:55 It's also good to know that people are also energetic machines.

02:59 We also run on energy. We get it from a different source.

03:02 We take chemical potential energy as a fuel and then we burn that energy and use that energy and each human being uses a certain amount of energy per unit time.

03:12 So a typical person, if they're in sort of a resting state and going about their normal business uses about 80 watts of power.

03:19 So in the course of a full day of 24 hours, if this is your average energy, or the average power rather you can find the amount of energy that that person used, that person needed from food based on just multiplying the power times the time.

03:33 So 80 watts times 24 hours in a day, if you put it all together, turns out to be about 2 kilowatt hours.

03:41 On the other hand, if you're moving a lot and being very active and exercising, you're going to use a lot more power, a lot more energy per unit time that you're going to need.

03:51 It turns out that for a very active person, you have maybe 400 watts of energy, of power rather being used, 400 watts meaning joules per unit time.

03:59 And finally, it's good to know that every person as they're doing this and using up energy is actually putting out energy.

04:06 So a given person standing in a room actually contributes energy to that room just in terms of the amount of heat energy leaving their body, etc.

04:15 So if you have a room full of people, it turns out that each person contributes some heat to that room based on the amount of power that they're consuming, the amount of energy that they're outputting.

04:26 And so a room full of people can actually be warmer and heated up as though it was a room full of light bulbs.

04:32 So again, the point here is to think about even people as we move forward to more practical examples as sources of and users of energy and they also take energy per unit time.

### About the Lecture

The lecture Power: Equations and Example by Jared Rovny is from the course Work.

### Included Quiz Questions

1. The work done, in units of energy, is equal to the applied power times the time.
2. The Watts used, in units of power, are equal to the applied power times the time.
3. The work done, in units of energy, is equal to the applied momentum times the time.
4. The Watts used, in units of energy, are equal to the applied power times the position times the time.
5. The work done, in units of energy, is equal to the applied power times the position times the time.
1. 20 hours
2. 200 hours
3. 20 minutes
4. 200 minutes
5. 2 hours
1. Joules
2. Watts
3. Hours
4. Kilograms
5. Kilograms∙Watts∙hours

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