Video: Stating the Formula Relating Charge, Current, and Time

Which of the following is the correct formula for the amount of charge flowing through a point in a circuit in a given time? 𝑄 represents the amount of charge, 𝐼 represents the current, and 𝑑 represents time. [A] 𝐼 = 𝑄𝑑 [B] 𝑄 = 𝐼/𝑑 [C] 𝑄 = 𝐼²𝑑 [D] 𝑄 = 𝐼𝑑

02:01

Video Transcript

Which of the following is the correct formula for the amount of charge flowing through a point in a circuit in a given time? 𝑄 represents the amount of charge, 𝐼 represents the current, and 𝑑 represents time.

In this example, we’re looking for the correct formula out of the four choices we’re given, A, B, C, and D, that represents the amount of charge, 𝑄, flowing through a point in a circuit over a given time. In other words, we want to know mathematically how it is that charge 𝑄, current 𝐼, and time 𝑑 are related.

It will be helpful to us to recall the general definition of just what a current is. Current is a measure of the amount of flowing material passing by a point in some amount of time. When it comes to electric current, that flowing material is charge. We represent that using the letter 𝑄. And we can represent some amount of time using the letter 𝑑.

Since current has to do with the amount of charge passing a point per unit time, we can divide 𝑄 by 𝑑. and that will give us the current, which we symbolize with 𝐼. We now have a mathematical equation for current. Let’s see if we find this equation anywhere among our answer options.

Looking first at answer option A, we see that that claims that current is equal to charge times time. But our equation shows that current is equal to charge divided by time. This means that option A is not the correct formula. All the remaining options after this one have 𝑄 isolated by itself on one side of the equation. In order to see how our equation compares, let’s algebraically rearrange it so that 𝑄 is on one side by itself.

To do this, we can take our equation and multiply both sides of it by the time passed 𝑑. When we do this, 𝑑 on the right-hand side of the equation cancels out since it’s in both numerator and denominator. Our equation now reads 𝑄, the charge, is equal to 𝐼 times 𝑑. And we see that, of the three choices B, C, and D, it’s D that matches up with this expression. So the correct formula for the amount of charge flowing through a point in a circuit over a given time is 𝑄 is equal to 𝐼 times 𝑑.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.