Moving Coil Galvanometer Explained Simply with Easy Examples

A moving coil galvanometer is a sensitive instrument that detects and measures very small electric currents. It works on the principle that a current-carrying coil placed in a magnetic field experiences a torque that turns it. The amount the coil turns, shown by a pointer moving over a scale, tells us how much current is flowing through the coil.

This instrument matters because it is the heart of almost all analogue electrical meters. With simple additions it becomes an ammeter or a voltmeter, and its working also teaches the basic idea behind the electric motor. Understanding its sensitivity shows how engineers build instruments that can reliably detect currents as tiny as a few microamperes.

Key Concepts

• Principle: a rectangular coil of N turns carrying current I in a magnetic field B experiences a torque that rotates it against the restoring torque of a spring.
• Radial magnetic field: curved pole pieces and a cylindrical soft iron core keep the field always parallel to the plane of the coil, so the deflecting torque stays proportional to the current at every angle.
• Deflecting torque: the turning effect produced by the magnetic force on the current-carrying sides of the coil.
• Restoring torque: the opposing torque from the twisted suspension or spring, proportional to the angle of deflection.
• Current sensitivity: the deflection produced per unit current, measured in radians per ampere or divisions per ampere.
• Voltage sensitivity: the deflection produced per unit voltage applied across the galvanometer terminals.

Formulas

The deflecting torque on the coil is τ = N I A B, where N is the number of turns, I is the current in amperes (A), A is the area of the coil in square metres (m²) and B is the magnetic field in tesla (T). Because the field is radial, this expression holds at all deflection angles. At equilibrium the deflecting torque balances the spring torque τ = k θ, where k is the torsional constant of the spring in newton-metres per radian and θ is the deflection in radians. This gives θ = (N A B / k) I, proving that deflection is directly proportional to current. Current sensitivity is S = θ / I = N A B / k, and voltage sensitivity is Sᵥ = S / R, where R is the coil resistance in ohms.

Worked Example

A galvanometer coil has 100 turns and an area of 1.5 cm². It is placed in a radial field of 0.4 T. The spring constant is k = 1 × 10⁻⁵ N·m/rad. Find the deflection when a current of 1 mA flows, and the current sensitivity.

1. Convert units: A = 1.5 cm² = 1.5 × 10⁻⁴ m², and I = 1 mA = 1 × 10⁻³ A.
2. Deflecting torque τ = N I A B = 100 × 10⁻³ × 1.5 × 10⁻⁴ × 0.4 = 6 × 10⁻⁶ N·m.
3. At equilibrium θ = τ / k = 6 × 10⁻⁶ / 1 × 10⁻⁵ = 0.6 rad, which is about 34 degrees, a clear and readable deflection.
4. Current sensitivity S = θ / I = 0.6 / 10⁻³ = 600 rad/A.

A current of just one milliampere turns the pointer by 0.6 radian, so even a current of a few microamperes produces a small but detectable movement. That is the secret of the galvanometer sensitivity.

Common Misconceptions

• More turns always make a better galvanometer. Wrong. More turns increase current sensitivity but also increase the coil resistance and mass. Voltage sensitivity may not improve, and the coil becomes slow and delicate.
• A galvanometer can measure large currents directly. Wrong. It is designed for microamperes to milliamperes. A large current would burn the fine coil wire, so a low-resistance shunt is connected in parallel to convert it into an ammeter.
• The pointer deflection depends on how the coil starts. Wrong. Because the field is radial, the torque is N I A B at every angle, so the scale is linear and each current gives one definite deflection.

Real-World Applications

The galvanometer movement is used in analogue ammeters, voltmeters and ohmmeters in school laboratories, workshops and older electrical panels. It serves as a null detector in Wheatstone bridge and potentiometer experiments, where the pointer sitting exactly at zero shows balance. Sensitive versions are used in recording instruments, insulation testers and earth resistance testers. Historically, galvanometers received telegraph signals and recorded earthquake tremors. The same balance of magnetic torque against a spring also appears in many vehicle dashboard gauges.

The moving coil galvanometer converts a tiny current into a proportional, visible deflection by balancing magnetic torque against a spring. Its current sensitivity, N A B divided by k, can be raised with more turns, larger area, stronger field or a softer spring, and with shunts and multipliers it becomes the ammeter and voltmeter used everywhere.