Permanent Magnet Moving Coil (PMMC) Instruments — Construction, Working & Torque Equation
The Permanent Magnet Moving Coil (PMMC) instrument is one of the most accurate and widely used measuring instruments in electrical engineering. It works on the principle that a current-carrying conductor placed in a magnetic field experiences a mechanical force. PMMC instruments are used exclusively for DC measurements and form the basis of analog multimeters, galvanometers, and precision laboratory instruments.
Principle of PMMC Instrument
A PMMC instrument operates on the D'Arsonval principle — when a current-carrying coil is placed in the magnetic field of a permanent magnet, it experiences a torque proportional to the current flowing through it. Since the magnetic field is constant (provided by the permanent magnet), the deflection of the pointer is directly proportional to the current, giving a uniform (linear) scale.
Construction of PMMC Instrument
As its name indicates, this instrument consists of a permanent magnet and a rectangular coil of many turns wound on a light aluminium or copper former. The main components are:
- Permanent Magnet: A U-shaped magnet made of ALNICO (Aluminium-Nickel-Cobalt alloy) or modern rare-earth materials provides a strong, uniform radial magnetic field.
- Moving Coil: A rectangular coil of fine enamelled copper wire wound on a lightweight aluminium former. The former also provides eddy current damping.
- Soft Iron Core: A cylindrical soft iron core is fixed between the magnetic poles to concentrate the flux and make the field radial and uniform.
- Control Springs: Two phosphor-bronze hairsprings spiralled in opposite directions provide the controlling torque and serve as current leads. Opposite spiralling neutralises the effects of temperature changes.
- Pointer and Scale: A lightweight aluminium pointer attached to the moving coil indicates the measured value on a calibrated scale.
- Bearings: Jewelled pivot bearings (sapphire) support the moving system with minimum friction.
Fig: Construction of a Permanent Magnet Moving Coil Instrument
Working of PMMC Instrument
When current passes through the coil, each side of the coil experiences a force according to the Lorentz force law (F = BIL). Since the two sides carry current in opposite directions, the forces create a couple that produces a deflecting torque. The coil rotates until the deflecting torque equals the restoring torque provided by the control springs.
Because the radial magnetic field ensures the plane of the coil is always parallel to the field, the torque remains constant for a given current regardless of the coil's angular position. This is why PMMC instruments have a uniform, evenly-divided scale.
Torque Equation & Derivation
Let us derive the deflecting torque produced in a PMMC instrument:
L = Length (depth) of coil (m)
b = Breadth of coil (m)
N = Number of turns
I = Current through the coil (A)
A = Face area of coil = L × b (m²)
Force on each side of the coil:
Deflecting torque (Td) = Force × perpendicular distance:
At equilibrium, deflecting torque equals controlling torque:
N × B × I × A = K × θ
θ = (NBA / K) × I
Since N, B, A, and K are all constants, deflection θ is directly proportional to current I. This confirms the linear scale of PMMC instruments.
Damping in PMMC Instruments
PMMC instruments use eddy current damping. When the aluminium former moves in the magnetic field, eddy currents are induced in it. These currents create a force opposing the motion (Lenz's law), bringing the pointer to rest quickly without oscillation. This is the most efficient form of damping and is a key advantage of PMMC instruments.
Advantages of PMMC Instruments
- Uniform (linear) scale — easy to read
- High torque-to-weight ratio — sensitive to small currents
- Low power consumption — does not load the circuit significantly
- Very effective eddy current damping — pointer settles quickly
- No hysteresis loss — permanent magnet field is constant
- Not affected by stray magnetic fields — strong internal field dominates
- High accuracy (±0.5% to ±2% of full scale)
- Can be used as ammeter, voltmeter, or galvanometer with appropriate shunts/multipliers
Disadvantages of PMMC Instruments
- Can measure only DC quantities — AC gives zero average deflection
- Costlier than moving iron instruments due to precision construction
- Errors develop with aging of permanent magnets and control springs
- Delicate construction — not suitable for rough handling
- Temperature variations affect spring stiffness and magnet strength
- Limited overload capacity — excessive current can damage the springs or burn the coil
Applications
- DC ammeters and voltmeters
- Ballistic galvanometers for charge measurement
- Analog multimeters (with rectifier for AC)
- Flux meters for magnetic flux measurement
- Precision laboratory measurements
- Panel meters in power supplies and battery chargers
PMMC vs Moving Iron — Comparison Table
Related Articles
- Moving Iron Instruments — Types & Working
- Deflecting Forces in Electrical Instruments
- Control Torque in Electrical Instruments
- Types of Damping Force in Electrical Instruments
- Hot Wire Instruments
Frequently Asked Questions
1. Why can't PMMC instruments measure AC?
In AC, the current reverses direction every half cycle. Since the deflecting torque is proportional to current, the pointer would try to deflect in both directions alternately. Due to the inertia of the moving system, the pointer cannot follow rapid reversals and shows zero average deflection. Hence, PMMC instruments work only on DC.
2. What is the function of the soft iron core in a PMMC instrument?
The cylindrical soft iron core serves two purposes: it concentrates the magnetic flux in the air gap (increasing flux density B), and it makes the magnetic field perfectly radial. A radial field ensures the torque is constant regardless of the coil's angular position, producing a linear scale.
3. How is a PMMC instrument used to measure AC?
By connecting a bridge rectifier circuit before the PMMC instrument, AC is converted to pulsating DC. The instrument then measures the average value of the rectified current. The scale is calibrated to show the RMS value (assuming a sinusoidal waveform). This is how analog multimeters measure AC voltage and current.
4. Why are two control springs wound in opposite directions?
The two phosphor-bronze springs are wound in opposite directions to compensate for temperature effects. If temperature changes the stiffness of one spring, the other spring (wound oppositely) experiences an equal and opposite change, keeping the net controlling torque constant and maintaining accuracy.
5. What is the difference between a galvanometer and a PMMC ammeter?
A galvanometer is a highly sensitive PMMC instrument designed to detect very small currents (microamperes). An ammeter is a PMMC instrument with a low-resistance shunt connected in parallel to extend its range to measure larger currents (milliamperes to amperes). Both use the same PMMC principle.