When analysing the operation of electrical and electronic circuits, or trying to understand why a circuit does not work as expected, eventually you will need to use a Voltmeter to measure the various voltage levels. Voltmeters used for the measurement of voltage come in many shapes and sizes, either analogue or digital, or as part of a digital multimeter more commonly used today.
Voltmeters can also be used to measure DC voltage as well as sinusoidal AC voltages but the introduction of a voltmeter as a measuring instrument into a circuit can interfere with its steady state conditions.
As its names implies, a “Voltmeter” is an instrument used for measuring voltage (V), that is the potential difference present between any two points within a circuit. To measure a voltage (potential difference), a voltmeter must be connected in parallel with the component whose voltage you wish to measure. Voltmeters can be used to measure the voltage drop across a single component or supply, or they can be used to measure the sum of voltage drops across two or more points or components within a circuit.
For example, if we connect a voltmeter across the terminals of a fully-charged automobile battery, it will indicate 12.6 volts. That is there is a difference in potential of 12.6 volts between the batteries positive and negative terminals. Thus voltage, V is always measured across or in parallel with a circuit component.
The most basic type of DC analogue voltmeter is the “permanent-magnetic moving-coil” (PMMC) meter, also known as a D’Arsonval movement. This type of analogue meter movement is basically a current measuring device (termed galvanometer) which can be configured to operate as either a Voltmeter or as an Ammeter, the principal difference is the way in which they are connected in a circuit. The moving-coil movement uses a fixed permanent magnet and a coil of very thin wire which is allowed to move (hence the name “moving-coil”) within the magnetic field of the magnet.
When connected to a circuit, an electrical current flows through the coil which inturn generates its own magnetic field (electromagnetism) that reacts against the magnetic field created by the surrounding permanent magnet thus causing the coil to move. Since the galvanometer responds to an internal flow of current, if we know the internal resistance of the coil (wound from copper wire), we can simply use Ohm’s law to determine the corresponding potential difference that is being measured.
Permanent Magnet Moving Coil Meter Construction
The amount by which the electromagnetic coil moves, called “deflection”, is proportional to the strength of current flowing through the coil needed to produce the magnetic field required to deflect the needle. Generally there is a pointer, or needle, connected to the coil so the movement of the coil causes the pointer to be deflected over a linear scale to indicate the value being measured with the deflection angle being proportional to the input current. Thus the pointer of a galvanometer moves in response to current.
Commonly thin helical watch movement type damping springs are used to control the angle of deflection preventing oscillations or rapid movements which could damage the pointer as well as keeping the movement of the coil in rest when no current passes through the coil. Generally the pointer movement is between zero on the left and full-scale deflection (FSD) at the far right of the scale. Some meter movements have a spring-centered pointer with the zero rest position being in the middle of the scale allowing for pointer movement in both directions. This is helpful for measuring voltage of either polarity.
Although this PMMC meter movement responds linearly to the flow of current in the moving coil, it can be adapted for measuring voltage by the addition of a resistance in series with the coils movement. The combination of a series resistance with the moving-coil meter movement forms a DC voltmeter which can give accurate results once calibrated.
Measurement of Voltage
We have seen in these tutorials that when electrical charges are in equilibrium, the voltage between any two points of a circuit is zero, and if a current (the movement of charge) flows around the circuit a voltage will exist between two or more different points of the circuit. Using a galvanometer, we can measure not only the current flowing between two points but also the voltage difference between them, as according to Ohm’s law, as these quantities are proportional to each other. Thus using a graduated voltmeter, we can measure the potential difference between any two points of a circuit.
But how do we convert a meter that works using a current to one that can be used to measure a voltage. We said previously that the deflection of the permanent magnet moving-coil meter is proportional to the strength of current passing through its moving coil. If its full-scale deflection (FSD) is multiplied by the moving coils internal resistance, the meter can be made to read a voltage instead of current, thus converting the moving magnet moving-coil meter into a DC voltmeter.
However due to the design of the coil movement, most PMMC meters are very sensitive devices which can have full-scale deflection current, IG ratings as low as 100µA (or less). If, for example, the moving coils resistive value RG is 500Ω, then the maximum full-scale voltage we could measure would be only 50mV (V = I*R = 100µA x 500Ω). So in order for the sensitive coil movement of a PMMC voltmeter to measure higher voltage values, we need to find some way of reducing the voltage being measured to a value the meter can handle and this is achieved by placing a resistor, called a multiplier, in series with the meters internal coil resistance.
Let’s assume that we wish to use our 100uA, 500Ω galvanometer above to measure circuit voltages upto 1.0 volt. Clearly we cannot connect the meter directly to measure 1 volt because as we have seen previously, the maximum voltage it can measure is 50 millivolts (50mV). But by using Ohm’s Law we can calculate the value of series resistor, RS required which will produce a full-scale meter movement when used to measure a potential difference of one volt.
Thus if the current for which the galvanometer gives full scale deflection is 100uA, then the series resistance RS required is calculated as 9.5kΩ. Thus a galvanometer can be converted into a voltmeter by simply connecting a large enough resistance in series with it as shown.
Voltmeter Series Resistance
Note that this series resistance, RS will always be higher than the coil’s internal resistance, RG to limit the strength of the current through the coil’s windings. The combination of the meter movement with this external series resistance then forms the basis of a simple analogue voltmeter.
Voltmeter Example No1
A PMMC galvanometer has an internal coil resistance of 100Ω and produces a full-scale deflection for 200 mV. Find the multiplier resistance required so that the meter gives a full deflection when measuring a DC voltage of 5 volts.
Therefore the series resistance required has a value of 2.4kΩ
We can use this method to measure any voltage value by changing the value of the multiplier resistors as required providing we know the the current or voltage full-scale deflection (FSD) values (IFSD or VFSD) of the galvanometer. Then all we need to do is re-label the scale to read from zero to the new measured voltage value.
This simple series-connected voltage divider circuit can be expanded further to have a range of different “multiplier” resistors within it design thereby allowing the voltmeter to be used to measure a range of different voltage levels at the flick of a switch.
Multi-Range Voltmeter Design
Our simple DC voltmeter from above can be further extended by using a number of series resistances, each one sized for a particular voltage range, which can be selected one-by-one by a single multi-pole switch thus allowing our analogue voltmeter to measure a wider range of voltage levels with a single movement. This type of voltmeter configuration is called a multirange voltmeter with the ranges selected dpending on the number of positions of the switch, for example, 4-position, 5-position, etc.
Direct Multi-range Voltmeter Configuration
In this voltmeter configuration each multiplier resistor, RS of the multirange voltmeter is connected in series with the meter as before to give the desired voltage range. So if we assume our 50mV FSD meter from above is required to measure the following voltage ranges of 10V, 50V, 100V, 250V, and 500V, then the required series resistors are calculated the same as before as:
Giving a direct multi-range voltmeter circuit of:
While this direct voltmeter configuration works very well for reading our range of voltages, the multiplier resistor values required to obtain the correct FSD of the meter for the calculated ranges can give resistive values that are not standard preferred values, or require resistors to be soldered together to produce the exact value. Our calculated values of 99.5kΩ through to 4.9995MΩ are not common resistor values, so we need to find a variation of the above voltmeter design which would use more commonly available resistor values.
Indirect Multi-range Voltmeter Configuration
A more practical design is the indirect voltmeter configuration in which one or more of the series resistances are connected together in a series chain with the meter to give the desired voltage range. The advantage here is that we can use standard preferred values for the multiplier resistors. So if we assume again our 50mV FSD meter and the voltage ranges of 10V, 50V, 100V, 250V, and 500V, then the required series multiplier resistors are calculated as:
Giving an indirect multi-range voltmeter circuit of:
Then we can see with this indirect 5-range voltmeter configuration, the higher the voltage to be measured, the more multiplier resistors are selected by the switch. The total resistance connected in series with the PMMC meter will be the sum of the resistances, as RTOTAL = RS1 + RS2 + RS3 … etc. Clearly then while the two circuits, direct and indirect voltmeter configuration are both able to read the same voltage levels, the use of standard and preferred resistor values of 400kΩ, 500kΩ, 1M5Ω, and 2M5Ω resistors make the indirect method easier and cheaper to construct.
Clearly, the choice of resistor values will ultimately depend on the FSD of the galvanometer used and the voltage levels that need to be measured. Either way a simple multi-range analogue DC voltmeter can be constructed by connecting higher series multiplier resistors and a switch. Most digital multimeters these days are auto-ranging.
One final point to note when building a DC voltmeter is that an ideal voltmeter will have no effect on the the part of the circuit or component being measured as it will have an infinite equivalent resistance. However in practice, when measuring voltages, connecting a voltmeter to a circuit, especially a high-resistance circuit, can reduce the effective resistance of the circuit and therefore has the effect of reducing the voltage being measured between the two points.
To minimise this loading effect a meter with a high sensitivity, that is, its full-scale deflection is achieved with a lower deflecting current should be used so that the multiplier resistance used for the voltmeter can be as high as possible to reduce the current that passes through the PMMC meter. The sensitivity of a voltmeter is measured in Ohms/Volt, (Ω/V).
