A man is replacing an incandescent light bulb in his house with a more
energy-efficient LED light. Before he changes the light bulb, he switches off the mains electricity in his
house. Why does he do this?
The idea here is that this man has an operating incandescent bulb that he wants to
switch out with a higher-efficiency LED light. One option for making the change would simply be to unscrew the incandescent bulb
while its plugged in and lit up and then screw in the higher-efficiency LED to be
done with the switch.
But instead, what he does is goes to the mains circuit breaker in his house and shuts
off the mains electricity so that this light bulb, along with all the other
electrical appliances in the house, turns off. It’s only then that the man goes over to the now-turned-off incandescent bulb,
unscrews it, and replaces it with the LED. And the question we want to answer is, why does he do it this way?
Well, think about the socket that these two light bulbs will be screwed in to. If we look at the base of that socket, we see where the end of the light bulb
electrically connects to a live wire in the wall. It’s this live wire which delivers the electricity, which in normal operation is able
to light up the light bulb. And typically, this is a safe situation because the light bulb is covering up the
live wire. Nothing else can get in contact with it, unless we remove the light bulb and expose
this live wire. That’s of course what happens when we change a light bulb.
If, while we were changing the bulb, we accidentally touch that live connection with
our finger, we would be delivered a painful electric shock. That’s of course if the mains electricity to the house is on. But if we turn them off, then there’s no danger of being shocked as we change the
bulb. This then is the reason why the man changes the bulb the way that he does.
We can write it out like this. We can say that if the man does not switch off the mains electricity, then if he
accidentally touches the live wire while changing the bulb, he will receive an
electric shock. So it’s about personal safety. That’s why the man changes the bulb this way. Moving on, let’s look a bit now into light bulb performance.
The incandescent light bulb that the man is replacing had an efficiency of just 2.7
percent. The incandescent light bulb had a power rating of 150 watts. The equation that relates the efficiency of an electrical device to its useful power
output and its total power input is efficiency is equal to useful power output
divided by total power input. Calculate the useful power output of the incandescent light bulb. Give your answer to two significant figures.
We can start on our solution to this question by creating a bit of a shorthand way of
writing out this equation for efficiency. We can replace efficiency with the letter capital 𝐸. We can write UPO in place of useful power output. And we can write TPI in place of total power input.
Clearing some space on screen then, here’s how we can now write this equation. We can write that the efficiency of an electrical device is equal to its useful power
output divided by its total power input.
Now in our case, we want to solve for the useful power output of this incandescent
light bulb. That means that, starting with this equation, we want to rearrange it algebraically
so that UPO is on one side by itself. Here’s how we’d do that. If we multiply both sides of this equation by the total power input, TPI, then
notice, on the right-hand side of this equation, that term appears in both the
numerator and the denominator, and so it cancels out. And this means we now have a useful equation for the useful power output. It’s equal to the total power input multiplied by the efficiency of our electrical
device. So for our incandescent light bulb, what is our efficiency and what is the total
Our problem statement tells us that the incandescent light bulb has a power rating of
150 watts. That means that’s how much power it takes in in order to operate normally. And then as far as efficiency, we’re told that that’s equal to 2.7 percent, meaning
that 2.7 percent of the total power input is actually converted to useful power
Notice that this tells us that almost 97 percent of the power input isn’t useful
power. In the case of our bulb, it goes to heating the environment rather than lighting
it. In any case, this is the efficiency of our bulb. But when we enter it into the equation, we’re not going to enter it in as a percent
as it’s written. Instead, we’ll enter it in as a decimal value.
Now what is 2.7 percent as a decimal? Well, if we have a number that’s written as a percent but we want to write it as a
decimal instead, then we take that number written as a percent, divide it by 100
percent, and our answer will be that value written as a decimal. So then in our case, we’ll take 2.7 percent and divide it by 100 percent, which gives
us the result 0.027. That’s 2.7 percent written as a decimal.
It’s that value that we’ll plug in for the efficiency 𝐸 in our equation. And we’re now ready to calculate UPO, the useful power output, of this incandescent
bulb. When we multiply these two numbers together and then round our answer to two
significant figures, like we’re asked, we get a result of 4.1 watts. This helps clarify just how inefficient an incandescent light bulb is. Of the 150 watts we used to power it, only 4.1 of those watts are useful power
output. This is a big part of the reason why incandescent light bulbs are often replaced with
higher-efficiency LEDs. Let’s move on to considering the cost of operating these two different types of
The LED light has a greater efficiency than the incandescent light bulb. How does the efficiency of the new light affect the cost of using the light? Give a reason for your answer.
So in this case, we’re comparing these two types of bulbs on the basis of their
efficiency, that is, how much useful power output they have for total power
input. We saw in the earlier example that the efficiency of an incandescent bulb is
somewhere around three percent. On the other hand, the efficiency of an LED bulb is roughly 80 percent, many times
more than the incandescent. This means that, for the LED bulb, about 80 percent of the power that we put in we
get out as useful power output, that is, light.
Let’s say that we wanted to get the same amount of light from each one of these
bulbs, the incandescent and the LED. In order to do that, the power that we would need to put into the incandescent bulb
would be much greater than the power we would need to put into the LED. That’s because of their differences in efficiency. That electrical power comes at a cost, a monetary cost, and that’s what our question
focuses on. It says, “How does the difference in efficiencies of these two bulbs affect their
cost of operation?”
Here’s what we can write about that. We can say that the cost of using the LED bulb is lower than the cost of using the
incandescent bulb because less energy is wasted as heat. For an equal bulb brightness, that is, an equal useful power output for the two
bulbs, the LED bulb generates much less heat than the incandescent one. In other words, it’s less wasteful, and therefore its cost of operation is lower.