Lesson video

Hello, my name is Dr.

Rowlandson, and today's lesson may save you a little bit of money in the future while also looking after the environment.

So let's get started.

Welcome to today's lesson from the unit of Maths and the Environment.

This lesson is called Solar Power, and by the end of today's lesson, we will be able to consider the implications of installing solar panels.

Here are some previous keywords that will be useful during today's lesson, so you may want to pause the video if you need to remind yourself what any of these words mean, and then press play when you're ready to continue.

During this lesson, we're going to look at how much money a household may spend on electricity, and then we're going to look at how much money could be saved if the house or property has solar panels.

Then finally, we're going to look at how much it costs to buy and instal solar panels, followed by working out how many years it would take to recover that cost with savings.

Let's start though by looking at calculating the cost of electricity.

Let's think about the cost of running a home such as a house or a flat.

The occupants of a home pay lots of different bills, and one of these bills is for the supply of electricity, but not everyone's electricity bill is for the same amount of money.

What factors could affect the amount of money that a household spends on electricity? Perhaps pause a video while you think of some examples and press play when you ready to continue together.

There are plenty of different factors that may affect the cost of an electricity bill.

Some of them involve the amount of electricity used.

For example, the size of a property could affect how much electricity is used to power the property.

The more rooms there are, the more electricity may be needed.

The number of occupants can also have an effect as well.

The more people there are living in a property, charging their own devices, watching TV and so on, the more electricity the household requires.

The number of appliances also apply in a similar sort of way.

Also how much time people spend at home.

If everyone leaves the house for six hours a day, for example, to go to work or school, then very little electricity is going to be used.

But if there are people working from home for example, then they're going to use electricity throughout the day and more electricity will be required.

So those are some examples that may affect the amount of electricity used and that will affect the cost of the bill.

But some factors may involve the cost of electricity itself.

For example, the cost per unit of electricity can vary between different energy supply companies, so can any additional fees as well.

And sometimes energy supply companies provide discounts for different ways of paying as well or discounts for other reasons.

Another thing that we're going to want to bear in mind during this lesson is that costs vary over time.

The cost electricity now is not the same as it was in the 1990s and the cost will change again in the future.

Also, the cost of equipment, materials and labour vary over time in a similar way, plus technology changes over time as well.

The performance and efficiencies of equipment may also improve due to advances in technology.

Let's take TVs for example.

A TV in the 1990s used a lot of electricity, but technology has improved over the years and now TVs use less electricity than they used to do and maybe in the future, they might use less electricity again.

We'll see this example when we think about solar panels.

Solar panels now produce so much electricity, but in the future they may become more efficient and produce even more electricity.

During this lesson you'll see lots of examples of costs and other numbers as well.

Now these numbers are all approximations based on averages from the UK in the year 2023.

So the actual figures may have changed over time depending on when you're doing this lesson.

Let's take this as an example here.

A typical one bedroom house consumes an average of 4.

9 kilowatt hours of electricity per day.

The kWh stands for kilowatt hours.

How much electricity would this be per month? Pause the video while you think about how we could calculate that and press play when you're ready to continue together.

Now I wonder what number you multiplied 4.

9 by, because a month can have 30 days in which you would have 147 kilowatt hours or 31 days, which you would have 151.

9 kilowatt hours or a month could have 28 days if it's February or 29 if it's February and a leap year.

So this calculation isn't quite so straightforward.

What you might want to do, because the majority months have 30 days or 31 days, you might want to use an approximation based on 30.

5 days per month.

We'll see an example of that later.

How much elasticity will be used in a year in this case? Pause the video while you think about this and press play when you're ready to continue together.

Once again, I wonder what you multiplied 4.

9 by because most years have 365 days, but a leap year as 366 days.

For this lesson, let's assume we're working with regular years, not leap years.

So in this case we'll do 4.

9 multiplied by 365, which gives you 1,788.

5 kilowatt hours, which is approximately 1,800 kilowatt hours per year.

Let's now calculate some costs.

In the year 2023, the average cost of electricity could be calculated using this formula here.

We could do 24.

5 pence per kilowatt hour consumed plus a 60 p daily standing charge.

Let's consider the two terms in this calculation separately.

The part on the left varies depending on how much electricity is consumed.

The more electricity is consumed, the more this amount was going to cost, but the term on the right is a constant.

It is paid every day regardless of how much electricity is used.

Even if no electricity is used whatsoever, you'll still need to pay your supplier company 60 p for that daily standing charge.

So let's now go back to our example of a typical one bedroom house that consumes an average of 4.

9 kilowatt hours of electricity per day.

How much would this cost per day? Well, we could calculate this by substituting 4.

9 in for the kilowatt hours consumed.

That means we do 24.

5 multiplied by 4.

9 plus 60 and that would give 180.

05 pence, which when we convert to pounds by dividing by 100, we would get approximately one pound 80 per day.

So how much would this cost per month then? And let's base our month on 30.

5 days.

To work this out, we could start in a similar way.

We could do 24.

5 multiplied by 4.

9, add 60, and that amount in the brackets is the cost per day.

And then let's multiply that by 30.

5 because there are approximately 30.

5 days in a month and that would give 5,491.

525, and that's pence.

When we convert that into pounds, we divide by a hundred and round to our nearest penny, and that would give us 54 pounds and 92 pence per month.

So how much would it cost per year? Well, we could do the same calculation, but rather than multiplying by 30.

5, we could multiply by 365 for 365 days in a regular year, and that would cost 65,718.

25 pence, which when we convert to pounds, we get 657 pounds and 18 pence when we round to the nearest pence.

Now in this case we have rounded down, but in some contexts involving costs, a company may choose to always round up to the next penny rather than rounding to the nearest penny, and this will be to ensure that they don't lose out on some money.

In other cases, a company may consider that approximately half the cost would round up and to the nearest penny and half the cost would round down to the nearest penny.

So overall the losses and gains would work themselves out in their own way.

For the sake of this lesson, let's always apply the normal rules of rounding.

So in this case, we'll round down to 657 pounds and 18 pence.

So let's check what we've learned.

A house with two to three bedrooms consumes on average 7.

9 kilowatt hours of electricity per day.

How much electricity would this be per year? And assume it's a regular year, not a leap year.

Give your answer rounded to two significant figures.

Pause the video while you work it out and press play for an answer.

We could do 7.

9 multiplied by 365 and that would give 2,900 kilowatt hours per year once we're rounded to two significant figures.

So now you have how to calculate the cost of electricity.

Could you please calculate how much the electricity would cost per day for this house? Pause the video while you work it out and press play When you're ready for an answer.

You could do 24.

5, multiplied by 7.

9 and then add 60, and that would give you two pound 54 pence per day once it's been rounded to the nearest penny.

How much would it cost per year? Pause the video while you work it out and press play when you're ready for an answer.

Now you might be tempted to take our previous answer of two pound 54 and multiply it by 365, but don't forget that answer was rounded.

So that would give you an approximate answer, but it's always more accurate to go back to our original calculation and do 24.

5 multiplied by 7.

9 plus 60 and then taking that and multiplying it by 365.

And then once you round that answer to the nearest penny, you should get 925 pounds and 46 pence per year.

So it's over to you then for task A.

This task contains one question and here it is.

Pause the video while you work these out and press play when you're ready for answers.

Okay, let's go through some answers.

This house would consume 4,307 kilowatt hours of electricity per year.

The cost per day would be three pound 49.

The cost per month based on 30.

5 days would be 106 pounds and 48 pence.

And the annual cost of electricity would be 1,274 pounds and 22 pence.

Now if you've got slightly different answers, it might be because you are using rounded numbers.

Just always check that you've used the whole calculation.

Well done so far.

Let's now move on to the next part of this lesson, where we're going to calculate the potential savings with solar panels.

Solar panels are a source of renewable energy.

They capture energy from the sun and convert it into electricity.

People can store solar panels on a roof to generate electricity and this electricity can be used by the occupants to reduce the amount of electricity that they require from an electricity supply company.

Now, in this picture we can see 19 solar panels, but the size of the property or the roof in particular determines how many solar panels can be installed, and panels also come in different sizes as well.

Now, a set of solar panels on one house may not produce the same amount electricity as a set of solar panels on another house.

So let's consider what factors may affect the amount of electricity that is produced by a set of solar panels on a property.

Perhaps pause the video and think about what these factors could be, and then press play when you're ready to continue together.

Well, there are lots of different factors, So let's take a look at just a few examples.

One could be the number of panels that are installed.

The more panels there are, the more electricity they're going to produce.

Another is the amount of sunlight that the panels get.

Remember, the panels need sunlight in order to create electricity.

So that means that things such as the location of the property is important because some countries get more sunlight per day than others.

Also, the directions that the panel face also may affect how much electricity they produce because a south-facing panel is going to be facing the sun for more time during the day than a north-facing panel.

Also, we need to consider any nearby obstructions that cast shade.

For example, if there are any taller buildings or trees that cast shade on the panels for a lot of the day, then they won't produce as much electricity.

And finally, how efficiently the panels convert sunlight into electricity, 'cause some panels are better than others.

We should also bear in mind that solar panels do not produce a constant amount of electricity throughout the year or even throughout a single day.

They produce the most amount of electricity during the middle of the day, where there is the most amount of peak sunlight.

They also produce more electricity in the summer than they do in the winter because there are more hours of sunlight.

Therefore, calculating the exact amount of electricity that a solar panel will produce per day can be difficult as conditions vary.

But what we could do is estimate the average amount of electricity that a solar panel could produce based on the average amount of peak sunlight it captures per day throughout the year.

The amount of electricity generated by a solar panel can be calculated Using this formula on a screen here.

Let's take a look at what these variables represent.

E is the amount of electricity produced by the panel, and that is measured in kilowatt hours.

P is the power rating of the panel, in other words, how efficient that panel is, and that's measured in kilowatts.

And H is the amount of peak sunlight that the panel receives during the day, and that is measured in hours.

And what we can see by the formula is we are multiplying P and H together.

P is measured in kilowatts, H is measured in hours and our overall units for the amount electricity is kilowatt hours.

So let's apply that formula now to this example here.

A house in the north of England has solar panels.

Each panel has a power rating of 350 watts.

On average it gets three hours of peak sunlight per day.

Now that doesn't mean that the sun only comes out for three hours a day and the rest of the day is in darkness.

What it means is the sun might be out for a long time for many, many hours, but there are three hours in the day where it is peak usable sunlight for the solar panel.

So based on this information, how much electricity does the panel produce per day on average? Now, Jacob has a few wise words here.

He says, "The amount of electricity will be an average because the calculation is based on average amount of sunlight." We're not going to be calculating any averages, such as a mean.

We are doing a calculation based on an average.

He says, "The actual amount of electricity it produces will fluctuate throughout the year as the amount of sunlight varies." So here's our formula, let's substitute some numbers in, but wait a minute before you do, because the power rating in the formula is measured in kilowatts, but the information gives us the power rating in watts.

So what we need to do first is convert 350 watts into kilowatts so that we can then substitute the kilowatts into our formula.

350 watts is equal to 0.

35 kilowatts because there are 1,000 watts in one kilowatt.

And now we have that, now we can substitute our numbers into the formula.

We can do 0.

35 multiplied by three to get 1.

05 kilowatt hours per day.

So let's check what we've learned.

What is 320 watts in kilowatts? Pause while you choose and press play for an answer.

The answer is B, 0.

32 kilowatts because we divide 320 by 1,000.

A house in the south of England has solar panels.

Each panel has a power rating of 320 watts.

On average, it gets 4.

2 hours of peak sunlight per day.

How much electricity does each panel produce per day on average? There's your formula, pause the video while you work it out and press play for an answer.

Well, first you need to convert 320 watts into kilowatts, which is 0.

32, and then substitute your information into your formula to get 1.

344 kilowatt hours per day.

So in ideal conditions, each solar panel would generate 3.

344 kilowatt hours of electricity per day on average, however, its performance is reduced by shade and its direction, so it produces approximately 20% less electricity than it would do in the ideal conditions.

How much electricity would this panel produce then? Give your answer accurate to three significant figures.

Pause the video while you work it out and press play for an answer.

What we are doing here is decreasing 1.

344 by 20%, a 20% decrease leaves 80% remaining.

So we can do 80% of 1.

344, and that would give approximately 1.

08 kilowatt hours when rounded to three significant figures.

Let's work through some more examples together now and see what else we can calculate.

A house has 12 solar panels in total, which we can see in the picture.

Each panel produces 1.

05 kilowatt hours of electricity per day on average.

However, the house typically consumes 14.

8 kilowatt hours of electricity per day.

So that means the solar panels do not generate enough electricity to cover all the energy requirements, so they still need to buy some electricity from the supplier company.

How much remaining electricity per day would the occupants need to consume from the electricity supplier company? Let's think about how we can do this.

First, we can work out the amount of electricity that is generated by the solar panels.

That is by doing 12, which is a number of panels, multiplied by 1.

05, which is the amount of electricity each one produces.

That means in total, they produce 12.

6 kilowatt hours per day of electricity.

So if the panels produce that much but they want 14.

8 kilowatt hours, we could do a subtraction to work out how much remaining electricity is required, and that gives 2.

2 kilowatt hours per day.

Let's consider how much this would cost.

The cost of electricity can be calculated using what you can see on the screen there.

The occupants of the house need to consume 2.

2 kilowatt hours of electricity per day from the energy supplier company.

Let's calculate the annual cost of electricity for this house now.

We could break this calculation down by first working out the cost per day and that'll be by substituting 2.

2 into our formula to give us 113.

9 pence per day.

And then if we multiply that by 365, we get the cost per year in pence, and then we can divide it by 100 to give it into pounds and round to the nearest penny, and that will give us 415 pounds and 74 pence per year.

So let's now think about how much money is saved here by the house having solar panels.

If the house did not have any solar panels and sourced all of its electricity from its energy supplier company, then the total cost would be 1,542 pounds and 49 pence per annum, and you can work that out using the information on the previous slides.

With the solar panels, the cost electricity is only 415 pounds and 74 pence per annum.

So how much money do these occupants save per year? We can work that out using a subtraction.

If we subtract our two amounts, we get 1,126 pounds and 75 pence.

So let's check what we've learned.

A house in the south of England has six solar panels.

Each panel produces 1.

08 kilowatt hours of electricity per day on average.

The house typically consumes 9.

8 kilowatt hours of electricity per day.

How much remaining electricity per day will the occupants need from the energy supplier company? Pause the video while you work this out and press play for an answer.

Here's our answer, 3.

32 kilowatt hours per day.

So here's how you work out the cost of electricity.

The house only needs 3.

32 kilowatt hours of electricity from its supplier company.

Could you please calculate the annual cost of electricity for this house? Pause while you work it out and press play for an answer.

Here we have the cost per day and then the cost per year.

Rounded to the nearest penny, it would be 515 pounds and 89 pence.

So if the house sources all of its electricity from its energy supplier company, the total cost will be 1,095 pounds and 37 pence per annum.

However, as you've just worked out, with the solar panels, it only costs 515 pounds and 89 pence per annum.

How much money do occupants save per year? Pause while you work it out and press play for an answer.

They save 579 pounds and 48 pence per year.

Okay, so to you then for task B.

This task contains one question and here it is.

Pause while you work it out and press play when you're ready for answer.

Okay, let's take a look at this together then.

Here we have the formula and the key information for this question.

Let's take a look at some of the numbers you might have encountered along the way while getting to your answer.

Here we have the cost of the electricity if it all came from the electricity supplier company, and this is the cost per year in pence.

Here we have the amount electricity produced by eight solar panels per day.

Here we have the remaining electricity that is required per day from the energy supplier company.

Here is the cost electricity per year when the solar panels are included, and here we have the amount of money saved per year and then it's given in pounds and pence as 917 pounds and 50 pence.

Well done so far, you're doing great.

Now, you might be thinking, fantastic, we can save loads of money on electricity bills by having solar panels.

But wait just a second, because solar panels cost money to buy and instal.

So in the final part of this lesson, we're going to look at the cost of buying and installing solar panels.

Solar panels can help reduce electricity bills, which we've seen already in this lesson, but they require an initial investment of money to buy and instal.

Let's consider what some of the factors might be that will affect the cost of buying and installing solar panels.

Pause the video while you think about this and press play when you're ready to look at some examples together.

Now there are many different factors that could affect how much money you spend here, but let's take a look at just a few examples.

One could be the price of the panels themselves because prices do vary depending on the types of panel you're buy, the brand or even the shops you're buying from.

Another thing to bear in mind is whether or not you buy any storage batteries.

Solar panels produce the most amount of electricity during the middle of the day, but you might not be home that time.

You might be at school or at work.

So what you may want to do is buy some storage batteries so that they can store electricity that they make in the day and then you can use it at night.

If you buy those batteries, it's gonna cost more money.

Also, there is other equipment involved in terms of installing solar panels, things like inverters and wiring.

You don't need to know what they are, but just do bear in mind, in fact, they will cost some extra money along the way as well.

And also, you may want to bear in mind labour costs.

If people are going to come to your home to instal the solar panels, they're going to charge you for their time, so that'll add up as well.

What we can see here is that the costs do add up, and it could be quite a lot of money that you spend initially on buying the solar panels and getting 'em installed in your home.

However, while there's quite a steep upfront cost, the solar panels do reduce your electricity bills.

So eventually the amount of money that you save in your electricity bills could add up to as much or if not more than the cost of installing them in the first place.

Let's take a look at an example.

The owners of a house are considering investing in solar panels.

They plan to buy a system with 12 panels.

The costs involved buying and installing the panels is displayed in the screen.

What will be the total upfront cost for doing this? Well, we can say the price per panel is 350 pounds and they're buying 12 panels, so we're going to multiply that 350 by 12.

The other things are all just single costs.

So we could do 350 times 12, add 5,000, add 1,500, add 1,200, and that'll give us 11,900 pounds to buy and instal the solar panels on this house.

That's quite a lot of money, but I wonder how long it would take to save enough money to cover that cost.

So in this example, the upfront cost of buying and installing the solar panels is 11,900 pounds.

But after they're installed, the house owner saves 1,126 pounds, 75 pence per year on their electricity bills.

How many years will it take for the annual savings to sum to more than the upfront cost of buying and installing the solar panels? We can work this out by dividing the amount of money that was spent on the initial investment by the amount of money that is saved per year, and that would give us 10.

561 years.

So that means after 11 years, they have made up the amount of money that they spent initially on the solar panels, and then after that amount of years, everything they have then is a saving.

So let's check what we've learned.

The owners of a house are considering investing in solar panels.

They plan to buy a system with six panels and the costs involved are displayed on the screen.

What will be the total upfront cost for buying and installing the solar panels? Pause while you work this out and press play for an answer.

The answer is 10,940 pounds.

So the total upfront cost is 10,940, but after they are installed, the house owner saves 917 pounds 51 pence per year on their electricity bills.

How many years will it take for the annual savings to sum to more than the upfront cost of buying and installing the panels? Pause while you work it out and press play for an answer.

It'll take approximately 12 years.

Okay, so to you then for task C, this task contains two questions and here is question one.

Pause while you work through it and press play for question two.

Question two has four parts, and here is part A.

Pause while you do this and press play for the rest of the parts of question two.

And here are parts B to D of question two.

Pause while you work through this and press play to look through some answers.

Okay, let's go through some answers.

For question one, it will cost 8,800 pounds to buy and instal a solar panels, but once they've done that, they will save 925 pounds per year.

That means it will take 10 years roughly to save enough money to cover the cost of the initial investment.

Then in question two, you're told that a house spends 1,400 pounds a year on electricity without solar panels.

They buy some solar panels, which costs 8,400 pounds to instal.

And once they're installed, the electricity bill is reduced to 300 pounds per year.

And in part A, you have to use that information to complete a table.

The middle row is the cumulative cost without the solar panels installed.

So every year we add 1,400 pounds onto that cost.

The bottom row is the cost initially that was spent to buy the panels, that was in year zero, 8,400 pounds, and every year, we'll go and add 300 pounds onto that.

We should get these values here.

Then for parts B and C, you had to take the information from the table and plot a graph of it.

For part B, you'd have the cost per year without the solar panels, it would look like this, and for part C, you would have the cost per year with the solar panels and that starts higher up on the vertical axes because you initially spend 8,400 pounds on the panels.

And then for Part D, you have to look at how many years it'll take for the solar panels to pay for themselves, that'll be with those two lines cross, and that would be 7.

6 years or eight years of we round up to the nearest year.

Fantastic work today.

Now let's summarise what we've learned.

Solar panels can reduce the cost of electricity bills, but they do require an upfront cost to buy and instal.

The size of the property will determine how many solar panels can be fitted onto it.

The amount of electricity generated by the panels vary depending on a bunch of different factors, such as the location, the direction they're facing, the amount of shade they get and so on.

And also it is possible to calculate when the solar panels have paid for themselves.

In other words, when you save enough money to cover the initial costs that you spent.

Well done today, have a great day.