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 𝑡 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 𝑡 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 𝑡.
Since current has to do with the
amount of charge passing a point per unit time, we can divide 𝑄 by 𝑡, 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 𝑡. When we do this, 𝑡 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 𝑡. 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 𝑡.