A 60-watt incandescent light bulb is left on for 30 seconds. In that time, it is supplied with 1800 joules of energy, but it only converts 36 joules of energy to light. What is the efficiency of the bulb?
So we’ve been asked to calculate the efficiency of something — in this case the light bulb. We’ve also been given values of the wattage of the bulb — 60 watts — and how long it was left on for — 30 seconds. We’re told that in the 30 seconds it was left on for, it’s supplied with 1800 joules of energy. But it only converts 36 joules of energy to light.
Now, in order to find out the efficiency, we first need to know what efficiency is. Efficiency is defined as the useful energy output divided by the total energy input. So we can plug in the values we’ve been given for the light bulb in order to find out its efficiency.
The useful energy output is the amount of energy converted to light, which happens to be 36 joules. The total energy input is 1800 joules. So we need to calculate 36 divided by 1800. And this turns out to be 0.02. But we can write this as a percentage as well simply by multiplying by 100 percent. And this way, we find that the efficiency of the light bulb is two percent.
Now, there are pieces of information in the question that we haven’t used, for example, the fact that the bulb is 60 watts and it was left on for 30 seconds. These pieces of information are irrelevant for an efficiency calculation. Yes, it’s true that we can calculate the total energy input by using these two values: 60 watts and 30 seconds because the energy supplied to the bulb can be calculated by multiplying the power of the bulb by the time for which it’s left on. And this happens to be 60 watts multiplied by 30 seconds, which ends up being 1800 joules.
But we’ve already been told this. So we don’t need the values of 60 watts and 30 seconds in this calculation at all. And this is something to be wary of. Some questions will give you values that you don’t need to use in the calculation. And this is done so that the question can test your understanding. It checks if you can think through the question and work out whether or not the answer that you’ve just calculated makes any sense. In this case, we’ve got an efficiency calculation. So it makes sense for the efficiency to be given as a percentage.
So remember if you come across any pieces of information that you haven’t had to use in the calculation, don’t panic. Sometimes you don’t need those pieces of information. Think through your working out and make sure you can convince yourself that those extra pieces of information are not needed.