Electricians need a variety of tools and equipment to go about their work, fixing wiring in houses and installing electrical appliances. One of the most important tools is a voltmeter or multimeter, which allows them to take readings of important quantities such as voltage or current. For example, high voltages can damage appliances, so checking the voltage reading helps to find dangerous faults. In this article, we're going to look closer at the Voltmeter, a fundamental instrument in circuit analysis, and see how they function and how to recognize them in circuit diagrams.
Voltmeter definition
When analyzing circuit diagrams or electrical components, we tend to focus on the three fundamental quantities, Current, Resistance, and Potential Difference. In this article, we're looking at voltmeters that measure potential difference, so let's recap what we mean by the potential difference.
Potential difference, or voltage, is a measure of the change in a charge's potential energy as it moves between two points in a circuit. The potential energy of a charge at a point defines the work done by an electric field in moving a charge to that point.
It's this potential difference between different points in the circuit which pushes charge around a circuit, creating a current. This initial potential difference is caused by an electromotive force (EMF) usually supplied by a cell or battery. Each component within a circuit changes the potential of the current, and so has an associated potential difference.
When considering conventional current, the potential difference of a cell or battery is positive, whilst the potential difference of the components is negative, as the potential of the current is 'used up' due to the resistance of the components whilst it flows around.
In circuit analysis, we often want to measure the potential difference of different components in a circuit, for example, to know how powerful a battery is. This can be done by using a Voltmeter.
A voltmeter is an instrument used to measure the potential difference across components in a circuit.
Voltmeter function and symbol
So, how exactly do voltmeters work, and what can we use them for? All voltmeters must be placed in parallel with the component they are trying to measure the voltage of. This is because components in parallel have the same potential difference, as per Kirchhoff's Loop Rule, and so by placing the voltmeter in parallel, it measures the voltage across the component by measuring its own voltage.
Different voltmeters do this in different ways. Early voltmeters measured the current flowing through them by using electromagnetic inductance to deflect a needle which, when combined with a resistor of known resistance, allowed the voltage to be calculated via Ohm's Law. Modern digital voltmeters tend to measure the discharge time of a capacitor to calculate the voltage across them.
Fig. 1 - An analog voltmeter uses electromagnetic induction to measure the potential difference.
As can be seen in figure 2, the symbol of a voltmeter in the circuit diagram is a circle with the letter V in the center.
Fig. 2 - The symbol for a voltmeter within circuit diagrams.
Voltmeters can measure the potential difference across any two points of a circuit, and so maybe in parallel with multiple components if the total potential difference of the components is being measured. For example, the voltmeter \(V_1\) measures the voltage of the bulb, but the voltmeter \(V_2\) measures the voltage of both the bulb and the resistor.
Fig. 3 - It's important to check which components are in parallel with the voltmeter as multiple components can be measured by the same voltmeter as seen above.
Voltmeters are designed to measure the voltage across with as little impact on the current through the component as possible. To ensure this, voltmeters have very high resistances to stop current flowing through them. When considering ideal voltmeters within circuit diagrams, they are assumed to have infinite resistance and so can measure the voltage without any current flowing through them. This is not possible for real voltmeters, and so voltmeters will always affect a circuit somewhat.
Consider a resistor with a resistance of \(20\,\mathrm{\Omega}\) with a current of \(100\,\mathrm{A}\) flowing through it.
By itself, the resistor has a voltage of \[V=20\,\mathrm{\Omega}\cdot 100\,\mathrm{A}=2000\,\mathrm{V}.\]
However, if this were measured with a voltmeter with a resistance of \(100\,\mathrm{\Omega}\) placed in parallel the combined resistance of the two components would be \[\begin{align}\frac{1}{R_{\text{total}}}=&\frac{1}{R_{\text{Resistor}}}+\frac{1}{R_{\text{Voltmeter}}}\\\\\implies R_{\text{total}}=&16.7\,\mathrm{\Omega}.\end{align}\]
So, the voltage across the resistor would now be \[V=100\,\mathrm{A}\cdot16.7\,\mathrm{\Omega}=1670\,\mathrm{V}.\]Hence a finite resistance voltmeter reduces the voltage of the component it is measuring.
Voltmeter unit
Voltage is defined as energy per unit charge and can be calculated using the equation\[\text{Voltage}=\frac{\text{Work Done}}{\text{Charge}}.\]
As energy is measured in joules \(\mathrm{J}\) and charge in coulomb \(\mathrm{C},\) it follows that the unit for voltage is joules per coulomb \(\frac{\mathrm{J}}{\mathrm{C}}\). This defines the standard unit of voltage, the volt \(\mathrm{V}=\frac{\mathrm{J}}{\mathrm{C}}\) named after the Italian physicist Alessandro Volta.
A volt is defined such that one \(1\,\mathrm{C}\) of charge increases its potential energy by \(1\,\mathrm{J}\) when moving through a potential difference of \(1\,\mathrm{V}\).
The voltage of a battery or power source determines how much energy it gives to a current, and so is an indicator of how powerful it is. In the USA, the mains electricity supply, used for household appliances like microwaves, runs at \(120\,\mathrm{V}\) whilst in much of the rest of the world, the mains are at \(240\,\mathrm{V}\). The sort of battery voltages you will see in circuit analysis, for example, during lab experiments, will likely be around \(5 \, \mathrm{to} \, 10\,\mathrm{V}\).
If a battery has a power output of \(100\,\mathrm{W}\) and powers a current of \(4\,\mathrm{A}\), what is the voltage of the battery?
Answer:
Recall the definitions of power and current are as follows
\[\begin{align}\text{Power}&=\frac{\text{Energy}}{\text{Time}}\\\\\mathrm{W}&=\mathrm{J}\,\mathrm{s}^{-1}.\\\\\text{Current}&=\frac{\text{Charge}}{\text{Time}}\\\\\mathrm{A}&=\,\mathrm{C}\,\mathrm{s}^{-1}.\end{align}\]
Hence, the voltage is given by \[\begin{align}\text{Voltage}&=\frac{\text{Power}}{\text{Current}}\\\\&=\frac{\text{Energy}}{\text{Charge}}.\end{align}\]
Plugging in the numbers gives\[\begin{align}\text{Voltage}&=\frac{100\,\mathrm{W}}{4\,\mathrm{A}}\\\\&=25\,\mathrm{V}.\end{align}\]
Voltmeter diagram
Voltmeters appear in many circuit analysis questions, so it's important that we can recognize voltmeters in a diagram as well as know how to construct diagrams with voltmeters in them. The key fact to remember is that voltmeters must be drawn parallel with whatever component or components they are measuring.
Let's take a look at an example circuit question involving voltmeters.
Consider the circuit in Figure 4 below. Determine the readings given by the voltmeters, \(V_1\) and \(V_2\).
Fig. 4 - Determine the values of \(V_1\) and \(V_2\) measured by the voltmeters in the circuit.
Recall that for parallel circuits, the voltage across each branch must be equal. As the battery voltage is \(15\,\mathrm{V}\), we know both branches will have a voltage of \(15\,\mathrm{V}\). The sum of the voltages of each component within a branch must then be equal to \(15\,\mathrm{V}\).
Looking at the first branch, we can use Ohm's Law to calculate the voltage across the bulb.
\[\begin{align}V&=IR\\&=0.5\,\mathrm{A}\cdot10\,\mathrm{\Omega}\\&=5\,\mathrm{V}.\end{align}\]
This tells us that
\[V_1=15\, \mathrm{V}-5\,\mathrm{V}=10\,\mathrm{V}.\]
Similarly, applying Ohm's Law to the resistor in the second branch gives us its voltage.\[\begin{align}V&=5\,\mathrm{A}\cdot2\,\mathrm{\Omega}\\&=10\,\mathrm{V}.\end{align}\]
Which tells us that\[V_2=15\,\mathrm{V}-10\,\mathrm{V}=5\,\mathrm{V}.\]
Voltmeter vs. Multimeter
You may be familiar with the instrument shown in Figure 5, from using them in lab work. These are multimeters and are often used to measure the voltage of a component, much like voltmeters. In fact, multimeters are simply instruments that can be used to measure multiple different electrical quantities, such as current, voltage, and resistance.
Fig. 5 - Multimeters are vital for electrical engineers, allowing different quantities to be measured with the same instrument.
Multimeters are essentially just an extension of single-use voltmeters and ammeters, which measure current. They contain multiple settings so that different quantities can be measured. However, placing multimeters in parallel with components is still necessary if we want to measure their voltage. A multimeter placed in series will not give a reading if on the voltage setting, though it would give a reading if on the current setting, as it would then act like an ammeter.
There is no specific circuit diagram symbol for a multimeter; instead, a voltmeter symbol would just signify that the multimeter should be used as a voltmeter in this position.
Voltmeter - Key takeaways
- Voltmeters are used to measure the potential difference between two points in an electrical circuit.
- Potential difference is a measure of the change in potential energy undergone by a test charge as it moves around a circuit.
- Voltmeters must be placed in parallel with the component it is measuring. They are designed to take divert as little current away as possible, hence having very high resistances. An ideal voltmeter has infinite resistance.
- Voltmeters measure the potential difference or voltage in units of Volts \(\mathrm{V}\) equivalent to \(\frac{\mathrm{J}}{\mathrm{C}}.\)
- Multimeters are instruments that can measure voltage, current, and resistance depending on which setting they are on.
References
- Fig. 1 - Voltmeter hg (https://commons.wikimedia.org/wiki/File:Voltmeter_hg.jpg) by Hannes Grobe (https://commons.wikimedia.org/wiki/User:Hgrobe) is licenced under CC BY-SA 3.0 (https://creativecommons.org/licenses/by/3.0/deed.en)
- Fig. 2 - Voltmeter symbol (https://commons.wikimedia.org/wiki/File:Voltmeter_symbol.png) by Guigui v.69 is licenced under CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)
- Fig. 3 Series circuit with voltmeter, StudySmarter Originals.
- Fig. 4 - Example voltmeter circuit, StudySmarter Originals.
- Fig. 5 - Digital Multimeter Aka(https://commons.wikimedia.org/wiki/File:Digital_Multimeter_Aka.jpg) by Aka (https://commons.wikimedia.org/wiki/User:Aka) is licenced by CC BY-SA 2.5 (https://creativecommons.org/licenses/by-sa/2.5/deed.en)
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