# How Does a Wattmeter Work? How Does It Measure the Power

Power is defined as the rate at which energy is transformed or made available. The power in a circuit at any instant is equal to the [product of the current in the circuit and the voltage across its terminal at that instant. The power in a dc circuit is best measured by separately measuring quantities V and I and by computing power by the formula P = VI. In the case of an AC circuit, the instantaneous power varies continuously as the current and voltage of through a cycle of values. If the voltage and current are both sinusoidal the average power over the cycle is given by the expression P = VI cos φ watts where V and I are the r.m.s. values of voltage and current.

A wattmeter is a device used to measure how much electrical power a circuit is producing, expressed in watts. It uses resistance to move a piece of metal, which is carefully calibrated along with a display with wattage numbers on it, the higher the wattage, the more the piece of metal will move. In this article, we will delve deeper into the inner workings of a wattmeter and understand how it measures and displays electrical power consumption.

## Working Principle of a Wattmeter

A wattmeter is used to measure either the power delivered by an electrical source or the power absorbed by a load. Wattmeter is the combination of both ammeter and voltammeter. A wattmeter has two coils, the current coil (CC) and the voltage coil (VC).

The current coil with very low resistance is connected in series with the load and responds to the load current, while the voltage coil is connected in parallel to the load circuit and responds to the load voltage. Depending on the test section (source or load), one terminal of each coil is shorted and connected either to the source or to the load.

In an AC circuit, a wattmeter is widely used to measure the single-phase and three-phase real power.

There are different types of wattmeters and they are given below:

### Dynamometer type wattmeter

A dynamometer is a device for measuring force, the moment of force (torque), or power. For example, the power produced by an engine, motor, or another rotating prime mover can be calculated by simultaneously measuring torque and rotational speed.

A dynamometer can also be used to determine the torque and power required to operate a driven machine such as a pump. In that case, a motoring or driving dynamometer is used. A dynamometer that is designed to be driven is called an absorption or passive dynamometer. A dynamometer that can either drive or absorb is called a universal or active dynamometer.

The fixed coil (current coil) is divided into two equal portions to provide a uniform field. It is designed to handle the full load current. The moving coil is used as a pressure coil. The fixed coil carries the current through the circuit and the moving coil carries the current proportional to the voltage across the circuit. High non-inductive resistance is connected in series with the moving coil to limit the current in the circuit. Since one flux is proportional to load current and the other is proportional to load voltage, the torque on the pointer or the moving coil is proportional to the power. The magnetic field of the fixed and moving coils reacts with one other causing the moving coil to turn about its axis.

The moving coil is carried on a pivoted spindle and the movement is spring controlled. The moving system carries a pointer and a damping vane, the latter moving in a sector-shaped box. The current coils are usually laminated when a heavy current is to be carried. Damping is provided by light aluminum vanes moving in air dashpot.

I₁ = main circuit current flowing through the fixed coil

I₂ = current proportional to the supply voltage

B = flux density

V = supply voltage

B ꝏ I1

and

B = K₁ I₁

Where K1 is a constant.

also

I₂ ꝏ V

I₂ = K₂ V

Where K₂ is another constant. The deflecting torque is given by,

Td ꝏ BI₂ ꝏ I₁V

Td = K VI₁ = K × Power

Where K is a constant. In a DC circuit, the power is given by the product of the voltage and current. Hence the torque is directly proportional to power. In ac circuit the mean deflecting torque Tm is given by,

Tm ꝏ VI cos Ɵ ꝏ True Power

Advantages

Some of the main advantages are given below:

1. It gives a very degree of accuracy.

2. Scale is not uniform.

3. It can be used on both ac and dc supplies.

Disadvantages

Some of the disadvantages are given below:

1. Errors due to voltage drop in the circuit.

2. Errors due to the current taken by the voltage coil.

### Induction type wattmeter

The induction-type wattmeter consists of two laminated electromagnets. One of them is excited by the load current of the main circuit, series, or current magnets, and its exciting coil (current coil) is connected in series with the circuit. The other is excited by a current proportional to the voltage of the circuit called a shunt magnet. Its exciting coil known as the voltage of the pressure coil is connected in parallel with the circuit. A thin aluminum disc is mounted in such a way that it cuts the fluxes of both magnets, and the deflecting torque is produced by the interaction between these fluxes and the eddy current which they induce in the disc.

The two or three copper rings are fitted on the central limb of the shunt magnet and can be adjusted to make the resultant flux in the shunt magnet lag behind the applied voltage by 90°. The two pressure coils are joined in series and are so wound that both send the flux through the central limb in the same direction. The series magnet also carries two coils joined in series and are so wound that they magnetize their respective magnetic cores in the same direction. The desired phase shift between the two magnet fluxes can be obtained by adjusting the position of the copper shading rings. The controlling torque in the induction wattmeter is provided by a spring fitted to the spindle of the moving system which also carries the pointer. The damping in these instruments is provided by the eddy current induced in the aluminum disc due to the fluxes produced by a permanent magnet.

The current coil carries the line current I₁ so that the flux produced by it is directly proportional to the line current I₁ and is in phase with it.

φ₁ ꝏ I₁

The pressure coil of the shunt magnet is made highly inductive, having an inductance L and negligible resistance. This is connected across the supply voltage V,

φ₂ ꝏ I₂ ꝏ V / ωL

Where,

ω = 2πf

f = supply frequency

φ₂ lags behind the supply voltage by 90°. Now let the load current I₁ lag behind V by an angle φ. Therefore, the phase angle between φ₁ and φ₂,

α = (90° – φ)

The Deflection torque acting on the aluminum disc is given by,

Td = K ω φ₁ φ₂ sin α

Where K is the constant. Now substituting the value of φ₁ and φ₂ in the above equation we get,

Td = K ω I₁ (V / ωL) sin (90° – φ)

Td = K’ V I₁ cos φ

Where K’ is constant,

Td ꝏ V I₁ cos φ ꝏ Power

The deflection torque is proportional to the power in the load circuit.

Advantages

Some of the advantages of the induction wattmeter are given below:

1. Have large scales

2. Can handle current up to 100 amperes.

3. Free from the effects of stray fields.

4. Practically free from frequency errors.

Disadvantages

Some of the disadvantages are given below:

1. Scale is not uniform.

2. Temperature errors.

3. Used only when the frequency and the supply voltage are constant.