# Voltmeter Multiplier – Construction and Calculation

A PMMC Instrument can be used as voltmeter by just connecting a series resistance with the moving coil. This series resistance is called Voltmeter Multiplier. This combination of moving coil and multiplier is connected across the point whose voltage is to be measured.

*There are two main functions of voltmeter multiplier:*

1) It limits the current through the PMMC moving coil to a value less than full scale deflection current and thus prevents moving coil from being damaged.

2) It minimizes the flow of current through the voltmeter and thus do not alter the circuit current whose voltage is to be measured. Ideally the resistance of voltmeter should be infinite.

**Calculation of Voltmeter Multiplier:**

The value of multiplier required to extend the voltage range is calculated as below.

Let,

I_{m} = Ifs = Full scale deflection current of meter

R_{m} = Internal resistance of meter

R_{s} = Multiplier resistance

V_{m} = Voltage across the moving coil

V = Full range voltage of meter

From the simplified voltmeter circuit given below,

V_{m} = I_{m}R_{m} ……………….(1)

and V = Im(R_{m} + R_{s}) ………….(2)

Dividing equation (2) by (1) we get,

V/Vm = 1 + R_{s}/R_{m}

Thus,

**m = Multiplying Factor = 1 + R _{s}/R_{m}**

The term V/V_{m} is called Multiplying Factor of Voltmeter. Multiplying Factor is basically the value by which the range of voltmeter can be extended. Let’s assume that the moving coil of voltmeter can sustain a voltage of 0.25 V and if we want to use it for measuring a voltage of 10 V then Multiplying Factor = 10/0.25 = 40. In this case the value of voltmeter multiplier which needs to connect in series with the moving coil can be calculated from equation (1) and (2). Let the value of internal resistance of meter R_{m }= 25 Ohm.

m = 1 + R_{s}/R_{m}

But m = 40 and R_{m} = 25

⇒ 40 = 1+R_{s}/25

⇒ 39 = R_{s}/25

⇒ R_{s} = 39×25 Ohm = 975 Ohm

Also, meter full scale deflection current = 0.25/25 = 0.01 A = 10 mA

Thus from the above example we observe that, to measure a voltage of 10 V (40 times greater than designed voltage) we need to connect a series resistance of 975 Ohm.

**Material of Voltmeter Multiplier:**

The essential requirements of voltmeter multiplier to fulfill are

- Their resistance should not change with time.

- Change in their resistance with temperature should be small

The resistance material used for multipliers is Manganin and constantan (copper nickel alloy).

Composition of Manganin, *Cu (84%) + Mn (12%) + Ni (4%)*