The moving coil galvanometer

The moving coil galvanometer detects and measures small currents. A coil sits in a strong radial magnetic field; current makes it turn, and a spring resists the turning.

The coil settles where the magnetic torque equals the spring's torque: NIAB = kφ, so the deflection is

φ = (NAB / k) × I: proportional to the current, so the scale is even.

Current sensitivity = φ/I = NAB/k (deflection per unit current). Voltage sensitivity = φ/V = NAB/(kR), where R is the coil's resistance.

Adding turns raises the current sensitivity, but it also raises R, so the voltage sensitivity may not rise at all.

A galvanometer is converted into the two everyday meters:

• Ammeter: connect a small resistance, a shunt S, in parallel. Most of the current bypasses the coil, and the meter's total resistance is very low, so it hardly changes the current it measures. It goes in series in the circuit.
• Voltmeter: connect a large resistance R in series. The total resistance is very high, so it draws almost no current. It goes in parallel across the part being measured.

Example: a galvanometer of 100 Ω gives full deflection at 1 mA.

• For a 1 A ammeter: S = I_g G / (I – I_g) = 0.001 × 100 / 0.999 ≈ 0.1 Ω in parallel.
• For a 10 V voltmeter: R = V/I_g – G = 10 000 – 100 = 9900 Ω in series.

An ideal ammeter has zero resistance and an ideal voltmeter infinite resistance. Real meters come close.