Video: Relating Charge and Current

Parth Gharfalkar

If the current through a point is _, then _ charge is passing through that point each second. [A] higher, less [B] higher, more [C] lower, more [D] lower, no.

02:53

Video Transcript

If the current through a point is blank, then blank charge is passing through that point each second: 1) higher, less; 2) higher, more; 3) lower, more; and 4) lower, no.

So this is a classic fill-in-the-blanks kind of question where we need to put the first word from the answer into the first blank and the second word for the second bank of course. And we need to think carefully about the relationship between, in this case, current and charge.

Specifically, what we’d be asked to do is to study how the current through a point affects the charge through that same point in each second. That means we’re looking for a relationship between current, charge, and time.

We can recall that the relationship we’re looking for is the definition of current. Current 𝐼 is equal to charge 𝑄 divided by time 𝑡. Or in words, the current is the rate of flow of charge. That means that current is the amount of charge that flows past the point per unit time.

So in this question, we’ve been told that the amount of time that we’re considering is 𝑡 is equal to one second. If we substitute that into our equation, we just get 𝐼 is equal to 𝑄 over one. So in other words, if we’re just considering one second of time, then the current passing through a point is the same as the charge passing through that point. But it is vital to remember that this only applies when the time is equal to one second.

Anyway, so we can see from what we’ve deduced that the current is directly proportional to the charge and, in fact, for one second, is equal to the charge. So logically speaking, if the current increases, for example, then the charge should also increase. If the current decreases, the charge should also decrease. That makes sense. They’re exactly the same, which means that we need to find the option that gives us this direct proportionality relationship.

So we can substitute in the words from options one to four into the blanks and see which ones make sense. Let’s try number one first. If the current through a point is higher, then less charge is passing through that point each second. That doesn’t make sense.

Let’s move on to number two. If the current through a point is higher, then more charge is passing through that point each second. That does make sense. That’s what we’ve just seen.

Number three, if the current through a point is lower, then more charge is passing through that point each second. Well, that’s kind of like option one flipped around. So no, that doesn’t make sense either.

And finally, number four, if the current through a point is lower, then no charge is passing through that point each second. Well, that’s not even close to making sense. So option two is our answer. If the current through a point is higher, then more charge is passing through that point each second.

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