Moving Coil Galvanometer

Think of the galvanometer coil like a weather vane — it rotates due to an applied force (magnetic torque) and comes to rest when the restoring spring force exactly balances that torque. The angle it settles at tells you how strong the wind (current) is.

It matters because:

• Serves as the foundation for constructing ammeters and voltmeters
• Used in laboratory circuits, electrical panels, and car dashboards (Weston type)
• Measures currents too small for standard ammeters to detect

A Moving Coil Galvanometer (MCG) is a sensitive electromagnetic instrument used to detect and measure small electric currents (of the order of microamperes to milliamperes) by measuring the deflection of a current-carrying coil placed in a uniform magnetic field.

Deflection produced per unit current.

Deflection produced per unit voltage.

The current required to produce a unit deflection (1 division) on the scale.

CS = \[\frac{\phi}{I}=\frac{NAB}{C}\]

Unit: div/A or div/μA

VS = \[\frac{\phi}{V}=\frac{NAB}{CG}\]

where G = resistance of the galvanometer coil.

Unit: div/V

k = \[\frac{I}{\phi}=\frac{C}{NAB}\]

k is the reciprocal of current sensitivity. A galvanometer with a smaller figure of merit is more sensitive.

When a current-carrying coil is placed in an external magnetic field, it experiences a magnetic torque that causes angular deflection proportional to the current.

In a radial magnetic field, θ = 90°, so sin⁡ θ = 1 at all positions. This gives:

Key Components

Step 1: Torque due to current (Deflecting Couple):

• When current I flows through a coil of N turns, area A, in a field B: τ_deflecting = N I A B (Since radial field: sin⁡90° = 1)

Step 2: Restoring Torque (Spring):

• The phosphor-bronze strip/spring opposes the deflection. If ϕ is the angular deflection and C (or k) is the torsional constant of the spring, τ_restoring = Cϕ

Step 3: Equilibrium Condition:

• At equilibrium, deflecting torque = restoring torque: NIAB = Cϕ

Step 4: Current–Deflection Relationship:

Principle: Connect a low-resistance shunt (S) in parallel to bypass excess current.

Circuit:

 

Formula:

Where:

• I_g​ = full-scale deflection current of the galvanometer
• G = galvanometer resistance
• I = maximum current to be measured

Key Points:

• Shunt S is very small — most current bypasses the galvanometer
• Ammeter has very low net resistance (ideal ammeter → 0 Ω)
• Connected in series in the circuit to measure current

Principle: Connect a high series resistance (R) in series to limit current.

Circuit:

 

Formula:

Where:

• V = maximum voltage to be measured
• I_g​ = full-scale deflection current

Key Points:

• The series resistance R is very large
• A voltmeter has a very high net resistance (ideal voltmeter → ∞ Ω)
• Connected in parallel across the component

Problem: In the circuit (Fig. 4.23), the current is to be measured. What is the value of the current if the ammeter shown is: (a) a galvanometer with a coil resistance R_G = 60 Ω, (b) a galvanometer converted to an ammeter by a shunt resistance r_s = 0.02 Ω, (c) an ideal ammeter with zero resistance?

The circuit consists of a 3 V source and a 3 Ω resistor.

(a) Galvanometer alone (coil resistance = 60 Ω)

Total resistance in the circuit = 60 + 3 = 63 Ω

(b) Galvanometer with shunt r_s = 0.02 Ω

Equivalent resistance of the galvanometer–shunt parallel combination:

Total circuit resistance = 3 + 0.02 = 3.02 Ω

(c) Ideal ammeter (zero resistance)

The three answers are: (a) 0.048 A, (b) 0.99 A, (c) 1.00 A.

The example illustrates that using a galvanometer directly (high resistance) severely reduces the measured current, while a properly shunted ammeter gives a reading very close to the ideal value.