The moving coil galvanometer

A moving coil galvanometer (MCG) has a many-turn coil free to turn about a fixed axis in a radial magnetic field. A soft iron core makes the field radial and stronger.

Because the field is radial, the plane of the coil is always along B and the torque is τ = NIAB. A spring gives a restoring torque kφ, where k is the torsional constant (restoring torque per unit twist).

At equilibrium kφ = NIAB, so the deflection φ = (NAB/k)I is proportional to the current. A pointer on the spring reads φ off a scale.

As a null detector (as in a Wheatstone bridge) the zero is at the centre of the scale and the pointer swings either way with the current's direction.

A bare galvanometer is a poor ammeter: it reaches full scale at currents of the order of μA, and its large resistance would change the current it is meant to measure.

Ammeter: add a small shunt rₛ in parallel. The combination has resistance R_G rₛ/(R_G + rₛ) ≈ rₛ, and most of the current goes through the shunt.

Voltmeter: add a large resistance R in series, so the meter's resistance is R_G + R ≈ R, large, and it draws very little current from the circuit it is connected across.

Current sensitivity φ/I = NAB/k; voltage sensitivity φ/V = NAB/(kR). Doubling N doubles the current sensitivity, but it also roughly doubles the coil's resistance, so the voltage sensitivity may not change.

Example 4.12: with a 3 Ω circuit on 3 V, a 60 Ω galvanometer as the meter gives I = 3/63 = 0.048 A; with a 0.02 Ω shunt the total is about 3.02 Ω and I = 0.99 A; an ideal ammeter would read 1.00 A.