Video Transcript
Three identical resistors are connected in series in a circuit. A voltmeter is used to measure the potential difference across all three of them. And it is found to be 18 volts. What is the potential difference across each resistor individually?
So in this question, we’ve got three identical resistors that are connected in series in a circuit. We’re told that a voltmeter is used to measure the potential difference or voltage across all three of them. And it’s important that it’s measuring across all three of them. And its potential difference is found to be 18 volts.
What we’re asked to do is to find the potential difference across each resistor individually. So let’s start by drawing a partial circuit diagram. So here are the three resistors in our circuit. Now we’ve got dotted lines either side because we don’t know what the rest of the circuit looks like. But we do know that there are three resistors connected in series.
Now the other thing that we know is that there’s a voltmeter connected across the resistors. And the voltmeter measures the potential difference across all three resistors. Therefore, we know that the voltmeter is connected here and here. And we can recall that voltmeters must be connected in parallel in order to measure the voltage across a component. So in this case, the voltmeter is measuring the voltage across all three resistors.
The voltmeter tells us that the potential difference across all three resistors is 18 volts. And this 18 volts must be equal to the potential difference across the first resistor, which we’ll call 𝑉 one, plus the potential difference across the second resistor, which we’ll call 𝑉 two, plus the potential difference across the third resistor, which we’ll call 𝑉 three. In other words, 𝑉 one plus 𝑉 two plus 𝑉 three is equal to 18 volts.
However, another piece of important information that we know is that the three resistors are identical. Therefore, the potential difference across each one of them should be the same. In other words, 𝑉 one is equal to 𝑉 two is equal to 𝑉 three. And just to make this simpler, let’s say that each one of them is equal to 𝑉. Let’s drop the subscripts.
So in our equation on the right, 𝑉 one is simply equal to 𝑉. 𝑉 two is simply equal to 𝑉. And 𝑉 three is simply equal to 𝑉 as well. What this tells us is that three 𝑉 is equal to 18 volts. And remember, this 𝑉 represents the voltage across each one of the resistors, whereas this V represents volts. So we can’t divide this equation by 𝑉 on both sides to give us three is equal to 18. That doesn’t make sense because the two 𝑉s are representing different things. This one is representing the voltage. And this one is representing the unit for voltage, which is volts.
So anyway, we can divide this equation instead by three on both sides. When we do this, we find that the threes on the left-hand side cancel out. And we can say that 18 divided by three is equal to six. So we say finally that 𝑉 is equal to six volts.
Now 𝑉 is the potential difference across each one of the resistors. So we’ve found our final answer. The potential difference across each resistor individually is six volts.
