# Video: Calculating the Amount of Energy Produced by Solar Panels per Year

A manufacturer makes a type of solar panel that has a power output of 290 W when exposed to direct sunlight. 8 of these solar panels are fitted to the roof of a house, which receives an average of 3.2 hours of direct sunlight per day over the course of a year. What is the total energy output of the solar panels on this house over the course of a year? Assume that there are 365 days in a year. Give your answer in kilowatt-hours to the nearest kilowatt-hour.

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### Video Transcript

A manufacturer makes a type of solar panel that has a power output of 290 watts when exposed to direct sunlight. Eight of these solar panels are fitted to the roof of a house, which receives an average of 3.2 hours of direct sunlight per day over the course of a year. What is the total energy output of the solar panels on this house over the course of a year? Assume that there are 365 days in a year. Give your answer in kilowatt hours to the nearest kilowatt hour.

Okay, so this is a really long question, which means we need to underline all the important bits so we don’t miss anything out. So first things first, we’re told that a manufacturer makes a type of solar panel that has a power output of 290 watts. And this power output is when the solar panel is exposed to direct sunlight. Now we’re also told that eight of these solar panels are fitted to the roof of a house. And the roof of this house receives on average 3.2 hours of sunlight — direct sunlight — per day and this is over the course of a year.

What we’ve been asked to do is to find the total energy output of the solar panels on the house over the course of a year. We’ve also been told to assume that there are 365 days in a year and we have to give our answer in kilowatt hours to the nearest kilowatt hour. So let’s label some of the quantities that we’ve been given in the question.

First of all, we know the power output of a solar panel. This power output is 290 watts, which we’ll call 𝑃. Now, it’s important to note that this power output only occurs when the solar panel is exposed to direct sunlight. Luckily for us, however, in the question, we’re told that the eight solar panels that are fitted on the house receive on average 3.2 hours of direct sunlight per day. Therefore, we’ve only been told how much direct sunlight the panels receive. And so we don’t need to worry about the fact that direct sunlight has been mentioned. Anyway, so eight of these panels are fitted onto a roof.

And we’ve also been told that the roof itself receives an average of 3.2 hours of direct sunlight every day and this is over the course of a year. In other words, every day on average, there’re 3.2 hours of sunlight and this has been measured over a year. Now of course, some days will be more sunny and some days will be less sunny. But on average, over a year, we find that there are 3.2 hours of direct sunlight per day on the roof.

Now what we’ve been asked to find is the total energy output by the solar panels — that eight solar panels on the roof — over the course of one year. We’ll call this 𝐸 sub year. And we need to give our answer in kilowatt hours to the nearest kilowatt hour. The last piece of information that we know is that we have to assume that there are 365 days in a year. Now, we might think “of course! there are 365 days in a year.” Well, not really, first of all, it could have been a leap year, which means that there is an extra day in the year. So there are 366 days.

But also in reality, the number of days in a year are slightly more than 365. It’s about 365 and a quarter days per year. That’s why we have leap years in the first place. We just say that three years have 365 days each and then the fourth year has 366 days to acount for that extra one-quarter days for each of the past four years. But anyway, so we’ve been told to assume that there are 365 days in a year.

Okay, so here’s one of our solar panels. And this converts light energy into 290 watts of power. That’s for one panel. But we know that on top of this roof that we’re studying, we’ve got eight of these panels. Therefore, the total power output which we’ll call 𝑃 sub tot is equal to 290 times eight because each panel produces 290 watts of power and we’ve got eight of these panels on the roof. Now, this happens to be 2320 watts.

However, since we need to give our final answer in kilowatt-hours, it’s best if we convert this power into kilowatts. We can do this by recalling that one kilowatt is equal to 1000 watts. But here, we have 2320 watts or in other words we have 2.32 kilowatts because we have 2.32 lots of 1000 watts and that’s the same as 2320 watts. And hence, 𝑃 sub tot the total power output of the eight solar panels combined is 2.32 kilowatts. So that’s the power of the panels. But we need to work out how much energy they’re putting out over the course of a year.

To do this, we can recall that power is defined as the energy per unit time. More specifically, it’s the energy transferred per unit time. Now, in the case of these solar panels, that’s the energy output by the solar panels divided by the time taken for this energy to be output. Now, we can use this equation to work out the amount of energy output by the panels every day.

To do this, we first multiply both sides of the equation by the time 𝑡. This way the time cancels on the right-hand side, leaving us with the time multiplied by the power is equal to the energy. Now, 𝑡 refers to the number of hours of sunlight we have every day and 𝑃 is the power output of the solar panels. Therefore, 𝐸 is the amount of energy output by the solar panels every day. So let’s call this energy 𝐸 sub day because that’s the amount of energy output every day.

So the amount of time for which the sun is shining on the solar panels every day is 3.2 hours as we’ve been told. And as we’ve worked out the total power of all the eight solar panels combined is 2.32 kilowatts. And hence, the product of these two quantities is going to give us the amount of energy output by the solar panels every day.

And we can look at the units very quickly. We’ve got hours and we’ve got kilowatts. So the unit of the final quantity when we multiply these two together is going to be hours times kilowatts or kilowatt hours. And this is what we want our final answer in. So we are working on the right lines anyway so the left-hand side evaluates to 7.424 kilowatt-hours. That’s the amount of energy we output from the solar panels every day.

So how much energy do we output every year? Well, if this is the energy output every day and we know that there are 365 days in one year, then we can say that the energy output per year is equal to 365 — that’s the number of days in every year — times the energy output per day. And happily for us, we already know what 𝐸 sub day is. So we can substitute in 7.424 kilowatt-hours. When we evaluate the product, we find that the amount of energy output by the solar panels every year is 2709.76 kilowatt-hours.

But we cannot stop here because remember we need to give our answer to the nearest kilowatt-hour. In other words, we need to round this digit here — the one just before the decimal. Now, it’s the one after the decimal that will tell us whether nine rounds up or stays the same. Well, this value here is a seven and that’s larger than a five. Therefore, this nine is going to round up to a 10. Well, yes, it’s going to become a 10. So we’ve got the zero here and there’s a one. But the one can carry forward into the tens column. And therefore, 2709.76 runs up to 2710 to the nearest whole number.

And at this point, we have our final answer. The total energy output of the solar panels on the house over the course of one year is 2710 kilowatt-hours to the nearest kilowatt-hour.