Video Transcript
A student sets up the circuit shown in the diagram. Initially, switch one is closed and switch two is open. If she opens switch one and closes switch two, will the current in the circuit increase or decrease?
In this question, we want to find out how the current changes when switch one is opened and switch two is closed. To determine the total current in a circuit, we can use Ohm’s law and rearrange the equation to make the current the subject of the equation. Doing this means we can write Ohm’s law as the current 𝐼 is equal to the potential difference 𝑉 divided by the resistance 𝑅. The potential difference in this circuit is fixed by the cell, which we will denote by 𝑉.
Let’s begin by considering the initial setup where switch one is closed and switch two is open and by labeling the resistors as 𝑅 one and 𝑅 two like so. When switch two is open, there will be no current through the resistor 𝑅 two. So the circuit can be simplified as follows. So in this circuit, the current in the circuit will be equal to the potential difference 𝑉 divided by the resistance 𝑅 one. When the student opens switch one and closes switch two, we will have the following circuit. Now there will be no current in the part of the circuit containing switch one. So we can simplify the circuit to look like the following.
As can be seen here, we now have two resistors in series. Therefore, the total resistance of the two resistors will be equal to 𝑅 one plus 𝑅 two. And so the new current through this circuit will be equal to the potential difference 𝑉 divided by 𝑅 total. Provided that the resistor 𝑅 two has nonzero resistance, this means that the denominator here will be larger than for the old current. Since we will be dividing by a larger number, this means that the new current will be smaller than the old current. Therefore, when the student opens switch one and closes switch two, the current in the circuit will decrease.
