In this explainer, we will learn how to use voltmeters in electric circuits to measure the potential difference across a component in the circuit.
Recall that when there is a potential difference between two points, this difference will exert a force on charges, resulting in a flow of charge between the points.
This is why electric potential difference is always measured between two locations. Recall that the flow of charges is electric current.
We can measure the electric potential difference across a component using a device called a voltmeter.
The unit of potential difference is the volt, which we give the symbol V. A potential difference of 1 volt, or 1 V, is equivalent to 1 joule of energy moving 1 coulomb of charge.
So, 1 volt is the same as 1 joule per coulomb.
The circuit symbol for a voltmeter is a circle with the letter V in the middle of it. This is shown in the diagram below.
Example 1: Finding the Number of Voltmeters in a Circuit
The diagram shows an electric circuit. How many voltmeters are there in the circuit?
Answer
The circuit symbol for a voltmeter is a circle with the letter V in the middle of it. This is shown in the diagram below.
There are two of these symbols in the circuit diagram we have been given; therefore, there are two voltmeters in the circuit.
There are other symbols in the circuit. What each symbol represents is shown below.
Example 2: Describing the Function of a Voltmeter
What quantity does a voltmeter measure?
Answer
In this question, we must write a short description of what a voltmeter measures. We must write a description that is clear and simple. We do not want to use more words than we really need to.
We can write the following, for example:
Consider the circuit shown in the diagram below.
This circuit consists of a bulb connected to a cell using wires. The cell supplies the potential difference.
The charges flow from one terminal of the cell, along a piece of wire, through the bulb, along another piece of wire, finally ending up at the other terminal of the cell. This is the only path the charges can take in this circuit.
The diagram below helps demonstrate this. The charges flow along wire 1 to the bulb.
The bulb uses this current to perform its function. It emits light. This means that there will be a potential difference between wire 1 and wire 2. This is the potential difference across the bulb.
Another way to think about this is that a potential difference is required to move the charges through the bulb.
In order to use a voltmeter to measure this potential difference, we must connect it to the circuit in a certain way.
We need to connect one end of the voltmeter to part of the circuit before the bulb, or wire 1.
The other end of the voltmeter must be connected to wire 2, or to part of the circuit after bulb.
Recall that potential difference is measured between two points; it is the difference in potential between them. Since we are measuring the potential difference across the bulb, we need to measure the difference in potential caused by the bulb only.
This is shown in the circuit diagram below.
This allows the voltmeter to find the potential difference across the bulb.
Charges flowing along the wire will now have two possible paths to travel along: either flowing through the bulb or flowing through the voltmeter.
These two paths are shown below.
Option A is one possible path for the charges to flow. Starting at the left terminal of the cell, they flow along the blue wire until they reach the branching point. The charges then flow along the green line, through the bulb, and to the right terminal of the cell along the blue line.
Option B is another possible path. Again, the charges start at the left terminal of the cell and flow along the blue wire. At the branching point, they instead flow along the red wire and through the voltmeter. They then flow to the right-hand terminal, along the blue wire.
When circuit components are placed along different paths like this, they are connected in parallel.
So, to measure the potential difference across a component, a voltmeter must be connected in parallel.
Specifically, if a path from one terminal of a cell to the other passes through two components without branching, those two components must be on this path.
However, if the current must branch in order to pass through both components, then the components must be on different paths.
Now consider the circuit below.
In this circuit, the voltmeter and the bulb are on the same path. There is only one path for the charges to flow.
The voltmeter is no longer measuring the potential difference across the bulb. This is because the voltmeter is only connected to the part of the circuit before the component.
When there is only one path between two components like this, they are connected in series. This is shown in the diagram below.
The only path the charges can follow is shown by the blue arrow. The charges start at one terminal of the cell, through the voltmeter, through the bulb, and back around to the other terminal.
A voltmeter cannot measure the potential difference of a component if it is connected in series.
The circuit diagram below shows a different location of the voltmeter.
There is also only one path for the charges to flow around this circuit, which is shown below.
This time, the charges, starting from the cell, flow through the bulb first and then the voltmeter. In this different position, the voltmeter is still in series with the bulb.
This means it cannot measure the potential difference across the bulb.
Example 3: Recognizing When a Voltmeter Is Connected Correctly
Each of the following diagrams shows a circuit containing a cell, a bulb, and a voltmeter. Which one shows how the voltmeter must be connected to the circuit in order to measure the potential difference across the bulb?
Answer
Recall that, for a voltmeter to measure the potential difference across a component, it must be connected in parallel with it.
This tells us that there must be two possible paths around the circuit. The voltmeter and the bulb must be on different paths.
First, consider option A. This cannot be the correct option as the circuit is broken. This means that there is only one path between the two terminals of the cell.
The voltmeter is only connected to the circuit after the bulb. It cannot measure the potential difference across the bulb.
Next, consider option B. The circuit diagram below shows the possible paths around the circuit for the charges to flow.
The wire has two paths, marked by A and B on the diagram. The bulb is on path A and the voltmeter path B.
The circuit branches where path A and path B meet each other. We see then that for charge flowing from one cell terminal to the other to pass through both the bulb and the voltmeter, the charge must flow along both path A and path B.
Charge that flows along path A cannot also flow along path B. Charge that flows along path B cannot also flow along path A.
This tells us that path A and path B are in parallel. We saw that the bulb is on path A and the voltmeter is on path B, and so, the voltmeter and bulb must be connected in parallel. This means that the voltmeter can correctly measure the potential difference across the bulb. So, B is the correct option.
We should also look at the other options. Option C has only one path, shown by the arrow in the diagram below.
This tells us that the voltmeter and bulb are in series. This means the voltmeter cannot measure the potential difference across it.
The same is true for option D: both the voltmeter and bulb are on the same path, as there is only one path around the circuit. They are in series. This is shown below.
Option E is a circuit with more than one path. However, the two components are not on different paths. This is shown in the diagram below.
Tracing the path of the wire counterclockwise around the circuit allows us to check if components are in series or in parallel. If the charges moving along a nonbranching path around the circuit can pass through both components, then these components are both on this path and so must be in series.
This is the case for option E: they are in series. In the diagram above of option E, starting at the cell, we can trace around to point i and, in one direction, go through the bulb.
We can then trace to point ii and along to the voltmeter. Moving to point iii and along to the cell completes the path.
Recall that a potential difference is measured between two points. So, to measure the potential difference across the bulb, we need our voltmeter to be connected to two different parts of the circuit: one before the component and one after. The voltmeter in option E does not have a connection to the circuit before the bulb, so it is not connected in parallel with it.
Example 4: Recognizing When a Voltmeter Is Connected Correctly to a Specific Component
Each of the following diagrams shows a circuit containing a cell, a bulb, a buzzer, and a voltmeter. Which one shows how the voltmeter must be connected to the circuit to measure the potential difference across the bulb only?
Answer
Recall that, for a voltmeter to measure the potential difference across a component, it must be connected in parallel with it.
This tells us that there must be two possible paths around the circuit; the voltmeter and the bulb must be on different paths.
Let us first consider option E. The voltmeter is connected in parallel to both the bulb and the buzzer.
We know this because they are on different paths, as shown in the diagram below.
The voltmeter is on path A. The other two components are on path B.
The circuit branches where path A and path B meet each other. We see then that for charge flowing from one cell terminal to the other to pass through the bulb, buzzer, and voltmeter, the charge must flow along both path A and along path B. This tells us that all components on path B, the bulb and the buzzer, are in parallel with all components on path A, the voltmeter.
The diagram also tells us that the buzzer and the bulb are in series as they are on the same path. In this case, charge flowing from one cell terminal to the other can pass through both the bulb and the buzzer while flowing along one path. This tells us they are in series with each other.
The question requires that the voltmeters measure the potential difference across the bulb only.
Because the voltmeter is parallel to both components, it will measure the total potential difference across both the bulb and the buzzer.
Next, we will consider option D. There are two paths around the circuit, as shown in the diagram below.
Tracing the path of the wire counterclockwise around the circuit allows us to check if components are in series or in parallel. If the charges moving along a nonbranching path around the circuit can pass through both components, then these components are both on this path and so must be in series.
In the diagram above of option D, starting at point i, we can trace around, in one direction, to point ii.
Then, we can trace along to point iii and to the bulb and buzzer.
The voltmeter is therefore not connected in parallel around the bulb, as they are both on this path. So, it cannot measure the potential difference across it.
Now, we consider option C. The possible paths around the circuit are shown in the diagram below.
This is similar to option E, but here, the voltmeter is on path B and the buzzer and the bulb on path A. This tells us that the voltmeter is connected in parallel with both the buzzer and the bulb.
The diagram also tells us that the buzzer and the bulb are, again, in series.
The question requires that the voltmeters measure the potential difference across the bulb only.
Recall that each side of the voltmeter must connect to a different side of the component measured. This must occur without passing through any other component before reaching the measured component.
This is not the case here, where path A passes through the other component before passing through the bulb.
Because the voltmeter is parallel to both components, it will measure the total potential difference across both the bulb and the buzzer.
The paths for option B are shown below.
The circuit branches where path A and path B meet each other. We see then that for charge flowing from one cell terminal to the other to pass through both the bulb and the voltmeter, the charge must flow along both path A and path B. Charge that flows along path A cannot also flow along path B. Charge that flows along path B cannot also flow along path A.
This tells us that path A and path B are in parallel. We saw that the bulb is on path A and the voltmeter is on path B, and so, the voltmeter and the bulb must be connected in parallel.
The buzzer is placed in the circuit before the branching. Therefore, it is not in parallel with the voltmeter and so its potential difference will not be measured, as required for the question.
This means that the voltmeter can correctly measure the potential difference across the bulb only. So, B is the correct option.
Example 5: Recognizing Equivalent Parallel Circuits with Different Layouts
Which two of the following circuits are equivalent?
Answer
The buzzer, bulb, and cell in each circuit do not move. In each diagram, it is just the voltmeter that changes location.
This tells us that two circuits will be equivalent if their respective voltmeters measure the same potential difference.
Recall that, for a voltmeter to measure the potential difference across a component, it must be connected in parallel with it.
Starting with option A, the diagram below shows the two paths around the circuit.
The circuit branches where path A and path B meet each other. We see then that for charge flowing from one cell terminal to the other to pass through both the bulb and the voltmeter, the charge must flow along both path A and path B. Charge that flows along path A cannot also flow along path B. Charge that flows along path B cannot also flow along path A.
The voltmeter is on path B, while the bulb is on path A. This means the two components are connected in parallel and the voltmeter will measure the potential difference across the bulb only.
In option B, the voltmeter is measuring the total potential difference across both the buzzer and the bulb. This is shown below.
The circuit branches where path A and path B meet each other. We see then that for charge flowing from one cell terminal to the other to pass through the bulb, buzzer, and voltmeter, the charge must flow along both path A and path B. This tells us that all components on path A, the bulb and buzzer, are in parallel with all components on path B, the voltmeter.
The buzzer and the bulb are both on path A, so they are in series, and the voltmeter is on path B and is connected in parallel to both components.
In option C, the buzzer and the voltmeter are on different paths. So, the voltmeter will measure the potential difference across the buzzer only. This is shown below.
The diagram below shows the possible paths around the circuit for option D. The voltmeter is on the same path as both the buzzer and the bulb.
Tracing the path of the wire counterclockwise around the circuit allows us to check if components are in series or in parallel. If the charges moving along a nonbranching path around the circuit can pass through both components, then these components are both on this path and so must be in series.
We start at the cell and move to point i. Then, we trace the path of the wire through the buzzer and through the bulb to point ii.
We then pass through the voltmeter. Finally, tracing around to the cell completes the path around the circuit.
This tells us that all three components are on the same path and so are in series. The voltmeter is not measuring the potential difference across any component.
Finally, option E has the possible paths shown in the diagram below.
The voltmeter is on a different path from the bulb, similar to option A but with the voltmeter on path A and the bulb on path B. This tells us they are connected in parallel to each to other and the voltmeter will again measure the potential difference across just the bulb.
Options E and A are the same.
Key Points
- A voltmeter is a device that can be used to measure the potential difference across a circuit component.
- The circuit symbol for a voltmeter is a circle with the letter
in the middle of it, as shown below.
- Voltmeters must be connected in parallel.
