# Types of Voltmeters with Voltage Calculation Equations

A voltmeter is an electrical component (voltage) measuring instrument that measures the amount of voltage at any two points in an electrical circuit. The units of voltage are volts and the measuring device is a meter that measures voltage by calibrating it to volts, millivolts (0.001 volts), or kilovolts (1,000 volts).

A voltmeter has a high internal resistance which is used in measuring the potential difference between two points of a circuit. In this way, the flow of current is controlled by the measuring instrument. This allows the device to take accurate readings of the voltage.

Symbol of Voltmeter

On the basis of the type of voltage voltmeter can be classified into the following two types:

• DC Voltmeter
• AC Voltmeter

## DC Voltmeter

A DC voltmeter is a DC voltage measuring instrument used to measure the DC voltage at any two points in an electrical circuit. If a resistor is connected in series with a Permanent Magnet Moving Coil (PMMC) galvanometer, the whole combination simultaneously acts as a DC voltmeter.

The series resistance, which is used in DC voltmeters, is also called series multiplier resistance or simply, the multiplier. It basically limits the amount of current flowing through the galvanometer to prevent the meter current from exceeding the full-scale deflection value.

This DC voltmeter is placed at two points of an electrical circuit where the DC voltage is measured.

Put KVL around the loop of the above circuit.

Where,

• Rse = The series multiplier resistance.
• = The full range DC voltage that is to be measured.
• Im = the full-scale deflection current.
• Rm = the internal resistance of the galvanometer.

The ratio of the full range DC voltage that is to be measured, V, and the DC voltage that falls in the galvanometer, Vm, is known as the multiplication factor M, it can be represented as,

From Equation 1, the following equation will be found for the full range DC voltage to be measured, V.

If the DC voltage drop across the galvanometer, Vm, is the value of the full-scale deflection current, Im and the internal resistance of the galvanometer, Rm, it can be represented as,

Substitute in Equation 3, Equation 4, and Equation 5.

The value of series multiplier resistance can be determined using Equation 2 or Equation 6 depending on the available data.

### Multi Range DC Voltmeter

In the previous section, a DC voltmeter is obtained by placing a multiplier resistor in series with the PMMC galvanometer. This DC voltmeter can be used to measure a particular range of DC voltage

If using a DC voltmeter to measure DC voltages of multiple ranges, multiple parallel multiplier resistors will have to be used instead of a single multiplier resistor and this entire combination of resistors is in series with the PMMC galvanometer.

The multi-range DC voltmeter is to be placed at two points of the electric circuit where the DC voltage of the required range is measured. The desired range of voltage can be selected by connecting switch S to the multiplier resistor.

m1, m2, m3, and m4 are the multiplier factors of the DC voltmeter. Then the full range DC voltage is measured at V1, V2, V3, and V4 respectively. Let us represent the corresponding formula for each multiplication factor as follows:

In the above circuit, there are four series multiplier resistors, Rse1, Rse2, Rse3, and Rse4. Write the corresponding formula for these four resistors as follows:

Using the above formulas one can find the resistance value of each series multiplier resistor.

## AC Voltmeter

The instruments used to measure AC voltage at any two points of an electric circuit are AC voltmeters. An AC voltmeter that has a rectifier is then a rectifier-based AC voltmeter.

DC voltmeter measures DC voltage only and if it is to be used to measure AC voltage, then it can be done by following two steps.

• Step1 − By converting the AC voltage signal into a DC voltage signal using a rectifier.
• Step1 − By measuring the DC or average value of the rectifier’s output signal.

### Types of Rectifier-based AC Voltmeters

The following are two types of rectifier-based AC voltmeters.

• AC Voltmeter Using Half Wave Rectifier.
• AC Voltmeter Using Full Wave Rectifier.

#### AC Voltmeter using Half Wave Rectifier

A half wave rectifier is connected next to a DC voltmeter, then that whole combination is called an AC voltmeter using a half wave rectifier.

In the above block diagram, there are two blocks, one half-wave rectifier, and the other DC voltmeter. Replacing each block with the corresponding component(s) in the above block diagram, one would obtain the corresponding circuit diagram:

The RMS value of the sinusoidal (AC) input voltage signal is,

Where,

• Vm = the maximum value of the sinusoidal (AC) input voltage signal.

The DC or average value of the output signal of a half wave rectifier is,

Put the value of Vm in the above equation,

The AC voltmeter will generate an output voltage that is equal to 0.45 times the RMS value of the sinusoidal (AC) input voltage signal.

#### AC Voltmeter Using Full Wave Rectifier

A full wave rectifier is connected next to a DC voltmeter, then that whole combination is done using a full wave rectifier called an AC voltmeter.

In the above block diagram, there are two blocks, one full wave rectifier, and the other a DC voltmeter. Replacing each block with the corresponding component in the above block diagram will yield the corresponding circuit diagram.

The RMS value of the sinusoidal (AC) input voltage signal is,

Where,

• Vm = the maximum value of the sinusoidal (AC) input voltage signal.

The DC or average value of the output signal of a full wave rectifier is,

Put the value of Vm in the above equation,

The AC voltmeter will generate an output voltage that is equal to 0.9 times the RMS value of the sinusoidal (AC) input voltage signal.

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