Measuring Instruments: Ammeters and Voltmeters

An ammeter measures current and is connected in series with a very low resistance, a voltmeter measures potential difference and is connected in parallel with a very high resistance; both are built from a sensitive galvanometer, with a shunt resistor in parallel for an ammeter and a multiplier resistor in series for a voltmeter. In brief: a real meter changes the circuit it measures, causing a loading error. A shunt of resistance R_s = I_gR_g ÷ (I − I_g) extends the range of a galvanometer to current I, and a multiplier R_m = V ÷ I_g − R_g extends it to voltage V. An ideal ammeter has zero resistance, and an ideal voltmeter has infinite resistance.

Multimeters measure current, voltage and resistance with one basic meter movement. This guide explains how the connections work, how to extend the range of a galvanometer, why loading errors occur, compares ammeters and voltmeters in a table, works through design and error calculations and corrects common mistakes.

What is a galvanometer?

A moving-coil galvanometer consists of a coil in the field of a permanent magnet, with a pointer and a spring. A current in the coil produces a torque, and the pointer deflects in proportion to the current until it is balanced by the spring. A typical instrument gives full-scale deflection (FSD) at a small current I_g (for example 50 µA) and has a coil resistance R_g (for example 100 Ω). On its own, it can measure only tiny currents and voltages (the voltage at FSD is I_gR_g = 5.0 mV in the example). Modern digital meters use an analog-to-digital converter instead of a moving coil, but the principles of connection and range extension are similar.

How is an ammeter made?

To measure larger currents, a low-resistance shunt R_s is connected in parallel with the galvanometer. Most of the current flows through the shunt, and only I_g flows through the coil at full scale. Since the voltage across both is the same: I_gR_g = (I − I_g)R_s, so R_s = I_gR_g ÷ (I − I_g). The resulting ammeter has a very low resistance (R_gR_s ÷ (R_g + R_s) ≈ R_s), so that it does not change the current in the circuit when it is connected in series. It must never be connected across a source, as the low resistance would draw a very large current.

How is a voltmeter made?

A galvanometer in series with a high-resistance multiplier R_m becomes a voltmeter. At full scale the total voltage V = I_g(R_g + R_m), so R_m = V ÷ I_g − R_g. The total resistance of the meter, V ÷ I_g, is large; a common specification is the resistance per volt (for example 20 kΩ/V). It is connected in parallel across the component, and draws only a small current. Digital voltmeters have input resistances of 10 MΩ or more.

What is the loading error?

An ammeter in series adds its resistance to the circuit, reducing the current slightly. A voltmeter in parallel draws some current and lowers the resistance between the two points, which reduces the voltage. The error is small when the ammeter resistance is much less than the circuit resistance and the voltmeter resistance is much greater than the resistance across which it is connected. The loading error is greatest in high-resistance circuits (voltmeter) and low-resistance circuits (ammeter). It can be reduced by choosing a meter with appropriate resistance or by correcting the reading.

Ammeters and voltmeters compared

Worked example: design and errors

1. Ammeter shunt. A galvanometer has I_g = 50 µA and R_g = 100 Ω. To measure up to 1.0 A: R_s = (50 × 10⁻⁶ × 100) ÷ (1.0 − 50 × 10⁻⁶) = 5.0 × 10⁻³ ÷ 0.99995 = 0.0050 Ω = 5.0 mΩ. The resistance of the ammeter is about 5.0 mΩ.
2. Voltmeter multiplier. To measure up to 10 V with the same galvanometer: R_m = V ÷ I_g − R_g = 10 ÷ 50 × 10⁻⁶ − 100 = 200,000 − 100 = 199,900 Ω. The meter has a resistance of 200 kΩ (20 kΩ per volt).
3. Voltmeter loading. Two resistors of 100 kΩ are in series across 10 V; the true voltage across each is 5.0 V. A voltmeter of resistance 200 kΩ connected across one of them gives a parallel resistance of 100 × 200 ÷ 300 = 66.7 kΩ. The reading is 10 × 66.7 ÷ (66.7 + 100) = 4.0 V, an error of 20 percent. A digital meter of 10 MΩ gives a parallel resistance of 99.0 kΩ and a reading of 10 × 99.0 ÷ 199.0 = 4.975 V, an error of 0.5 percent.
4. Ammeter loading. A 1.0 Ω resistor is connected to a 1.5 V cell (negligible internal resistance). The true current is 1.5 A. An ammeter of resistance 0.10 Ω in series gives I = 1.5 ÷ 1.10 = 1.36 A, an error of 9 percent. An ammeter with a resistance of 0.005 Ω would give 1.4925 A, an error of 0.5 percent.
5. Reading the scale. A voltmeter with a range of 0 to 10 V and 100 divisions has a resolution of 0.10 V. Reading a pointer halfway between two divisions gives an uncertainty of ±0.05 V.

How were meters developed?

Hans Christian Ørsted’s discovery (1820) that a current deflects a compass led Johann Schweigger to build the first galvanometer the same year. Jacques-Arsène d’Arsonval and Marcel Deprez developed the moving-coil meter in 1882, and Edward Weston improved it into a robust, portable meter in the 1880s. The digital multimeter, in the 1970s, replaced the pointer by a numerical display.

Which mistakes are common?

Mistake 1: Connecting an ammeter in parallel

Because of its tiny resistance, it can draw a large current, damaging the meter or the source.

Mistake 2: Assuming that meters are ideal

Real meters have a resistance, and it affects the readings, especially in high-resistance circuits.

Mistake 3: Using the wrong range

Start with the highest range when the value is unknown to avoid overloading the meter.

Mistake 4: Connecting a meter with the wrong polarity

Analog meters deflect backward. Connect the positive terminal to the point at higher potential.