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 $43 mV$ ($1 mA \times 43 Ω$), $43 Ω$ 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. 1].
Basic voltmeter.
Fig. 1: Basic voltmeter.
Multirange voltmeter.
Fig. 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. 1], we obtain
$$[10 V - (1 mA)(Rseries)] - 43 mV = 0$$
$$R_{series} = 10 V - (43 mV) 1 mA = 9957 Ω =10 kΩ$$
In general,
$$\bbox[5px,border:1px solid grey] {R_{series} = {V_{max} - V_{VS} \over I_{CS}}} \tag{1}$$

How multirange voltmeter is designed?

One method of constructing a multirange voltmeter is shown in [Fig. 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 $100 V$,
$$R_{series} = 50 kΩ + 40 kΩ + 10 kΩ = 100 kΩ$$

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