Current due to closing a switch: worked example | DC Circuits | AP Physics 1 | Khan Academy

We are asked how does the current through R1 behave when the switch is open compared to the current through R1 when the switch is closed. Pause this video and see if you can figure that out.

All right, so let's just think about the two scenarios. We could view the current as this right over here, this current that we care about. We could either measure it there, or you could measure it right over there.

Let's first think about the scenario where the switch is open. Our current, when our switch is open, is going to be equal to the voltage across the resistors, and that's going to be our 12 volts. Twelve volts divided by the equivalent resistance of these resistors when the switch is open. Essentially, we just have R1 and R2 in series, and so this is just going to be R1 plus R2. If you have two resistors in series, their equivalent resistance is just the sum of their resistances. Fair enough?

Now, let's think about the situation where the switch is closed. So here, our current at this point of our circuit, or the current going through R1, so I sub closed, is once again going to be equal to 12 volts—the voltage across the resistors. But what are we going to divide by now?

When we close the switch, what happens? Well, these lines where we see no resistors in circuit diagrams—that's assumed to be resistanceless. So, all of the current will actually flow that way. By closing this switch, you're essentially removing R2 from the circuit. The current will just go through R1 and then follow the path of least resistance—literally.

In this situation, our current is going to be 12 volts divided by essentially just one resistance, divided by R1. So when you closed the circuit, you've essentially taken a resistor out, and so if you took a resistor out, you're going to increase the current. You could just write it as the current when the switch is open is going to be less than the current when the switch is closed.

Once again, why is that? Well, just look at the denominators here. When the switch is open, you're dividing by a larger number than when the switch is closed. Or another way of thinking about it, when the switch is open, the R2 resistance is factored in. When the switch is closed, the R2 resistance essentially becomes a non-factor, and you have less resistance, which would mean you would have higher current.