Voltmeter Design

A variation in the additional circuitry permits the use of the iron-vane movement in the design of a voltmeter. The 1 mA, 43 Ω movement can also be rated as a 43 mV (1 mA x 43 Ω), 43 Ω movement, indicating that the maximum voltage that the movement can measure independently is 43 mV. The millivolt rating is sometimes referred to as the voltage sensitivity (VS). The basic construction of the voltmeter is shown in Fig.no.1.
Basic voltmeter.
Fig.no.1: Basic voltmeter.
Multirange voltmeter.
Fig.no.2: Multirange voltmeter.
The $R_{series}$ is adjusted to limit the current through the movement to 1 mA when the maximum voltage is applied across the voltmeter. A lower voltage simply reduces the current in the circuit and thereby the deflection of the movement. Applying Kirchhoff's voltage law around the closed loop of Fig.no.1, we obtain $$[10 V - (1 mA)(Rseries)] - 43 mV = 0$$ or $$R_{series} = 10 V - (43 mV) 1 mA = 9957 Ω =10 kΩ$$
In general, $$\bbox[5px,border:1px solid blue] {\color{blue}{R_{series} = {V_{max} - V_{VS} \over I_{CS}}}} \tag{1}$$

How multirange voltmeter is designed?

One method of constructing a multirange voltmeter is shown in Fig.no.2. If the rotary switch is at 10 V, $$R_{series} = 10 kΩ$$ at 50 V, $$R_{series} = 40 kΩ + 10 kΩ = 50 kΩ$$ and at 100 V, $$R_{series} = 50 kΩ + 40 kΩ + 10 kΩ = 100 kΩ$$