Video Transcript
A laptop charger passes a current of 5.0 amps through a laptop battery. Over a period of time, 45000 coulombs of charge is transferred to the battery. For how many hours was the laptop left to charge?
Alright, in this question, we’ve got a laptop charger, which passes a current of 5.0 amps through a laptop battery. As time progresses, eventually 45000 coulombs of charge is transferred to the battery. What we’re asked to do is to work out for how many hours the laptop was left to charge. In other words, we have to work out an amount of time.
So we need to find out a relationship between the current through a laptop battery, the charge transferred to the battery, and the amount of time for which the laptop was left to charge.
The relationship that we’re looking for is the following. The current 𝐼 is equal to the charge transferred 𝑄 divided by the time for which the charge was transferring 𝑡. In other words, current is a rate of transfer of charge. It is the amount of charge transferred per unit time.
And remember, the standard units for each one of these quantities is that current is measured in amps, charge is measured in coulombs, and time is measured in seconds. So since we’ve been given a current in amps and a charge in coulombs, we can work out the amount of time taken. But this will be in seconds.
However, the question wants us to work out the number of hours. So we can work out the time in seconds and then convert it to hours. So let’s go about doing that.
First of all though, we need to rearrange the equation. We’re trying to solve for 𝑡, the time. So what we need to do is multiply both sides of the equation by 𝑡 over 𝐼. On the left-hand side, the currents cancel out. And on the right-hand side, the times cancel out, leaving us with 𝑡 is equal to 𝑄 over 𝐼.
Now what we can do is to plug in the values of 𝑄 and 𝐼 that we’ve been given in the question, which ends up being 45000 coulombs divided by 5.0 amps. And this fraction evaluates to 9000. Now, remember, we’re calculating the amount of time for which the laptop was left to charge. And as we said earlier, the standard unit of time is seconds.
So now that we know the time in seconds, we want to convert this to a time in hours. To do this, we first need to recall that, in one minute, there are 60 seconds. And in every hour, there are 60 minutes. So we can combine these two pieces of information to give us the number of seconds in one hour.
There are 60 times 60 seconds in one hour, because if each minute has 60 seconds in it and every hour has 60 minutes in it, then there will be 60 times 60, 3600 seconds, in one hour. Now if one hour has 3600 seconds in it, then how many hours are equivalent to 9000 seconds?
To do this, we need to calculate the total number of time, which is 9000 seconds, divided by the number of seconds in every hour. This will give us a time in hours. And once we evaluate this fraction, we find that it’s equal to 2.5 hours. And hence we’ve reached our final answer. The laptop was left to charge for 2.5 hours.
