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

Video Transcript

Which of the following is the correct formula for the current through a point in a circuit? 𝐼 represents the current, 𝑄 represents the amount of charge, and 𝑡 represents time. (A) 𝐼 is equal to 𝑄 divided by 𝑡. (B) 𝐼 is equal to 𝑄 multiplied by 𝑡. (C) 𝐼 is equal to 𝑡 divided by 𝑄. (D) 𝑄 is equal to 𝐼 multiplied by 𝑡 squared.

In this question, we want to find the formula for the current through a point in a circuit. We will begin by recalling the definition for electric current.

Electric current is the rate at which electric charge passes a point in a circuit. When an amount of charge 𝑄 passes a point in the circuit in a time 𝑡, the current 𝐼 is given by 𝐼 is equal to 𝑄 divided by 𝑡. This corresponds to option (A). We can confirm that this equation is correct by looking at the units for each of these quantities.

Units are an important part of every physics problem. Not only do they communicate the exact type of quantity we are working with, but they can also include clues to help solve the problem. The SI unit for charge is the coulomb, which is denoted by a capital C. The SI unit for time is the second, which is denoted by a lowercase s. The SI unit for current is the ampere, which is denoted by a capital A. One ampere is equal to one coulomb per second.

Looking at the formula 𝐼 is equal to 𝑄 divided by 𝑡 in option (A), we see that the left-hand side has units of amperes and the right-hand side has units of coulombs divided by seconds. We know that the ampere is equal to one coulomb per second. So we can see that the units match on both sides of this equation.

Now let’s think about the units of the other options we’ve been presented with. Looking at the formula 𝐼 is equal to 𝑄 multiplied by 𝑡 in option (B), we see that the left-hand side has units of amperes and the right-hand side has units of coulombs multiplied by seconds. Since amperes are equal to coulombs per second, we can substitute this in on the left-hand side. This gives us that coulombs divided by seconds equals coulombs multiplied by seconds. We can now see that the units on both sides of this equation do not match. This means that this formula is incorrect, and so option (B) is incorrect.

Looking at the formula 𝐼 is equal to 𝑡 divided by 𝑄 in option (C), we see that the left-hand side has units of amperes and the right-hand side has units of seconds divided by coulombs. Replacing amperes with coulombs per second, we see that the left-hand side becomes coulombs divided by seconds. Again, we see that the units on both sides of this equation do not match. This means that this formula is incorrect, so option (C) is incorrect.

Looking at the formula 𝑄 is equal to 𝐼 multiplied by 𝑡 squared in option (D), we see that the left-hand side has units of coulombs and the right-hand side has units of amperes multiplied by seconds squared. Replacing amperes with coulombs per second and simplifying, we find that the right-hand side becomes coulombs multiplied by seconds. Again, we see that the units on both sides of this equation do not match. This means that this formula is incorrect, and option (D) is incorrect.

And so we can confirm that option (A) is indeed the correct answer. 𝐼 is equal to 𝑄 divided by 𝑡 is the correct formula for the current through a point in a circuit.