# Wattmeter: operation and main types

Fulfilling the request, This post’s subject is wattmeter operation. An instrument that measures provided or dissipated power in a circuit.

## Electrodynamic wattmeter

Operates with a moving coil, the voltage inductor, and 2 static coils, connected in series, voltage inductors. The moving or pressure coil is linked to a pointer with a spiral spring. The current fixed coils generate a magnetic field when receiving electric current. When current passes through the moving inductor, a torque is generated on it and the pointer moves. The voltage inductor has an iron core, not shown in this image. Source: Fundamentos de Eletricidad. Wattmeter circuit, the R resistor serves to limit current on pressure coil. V is the voltage provided by the source and the load receives the power. Circuit model on the left. Source: 4S6GGS.

This type of wattmeter can measure powers in DC and AC. It’s also used in calibration due to high degree of precision.

### Measurement in direct current

The equation of deflection torque $T_{d}$ on the moving inductor’s pointer.

$T_{d}=i_{c}i_{p}\frac{\delta M}{\delta \theta }$

• $i_{c}$ and $i_{p}$ are the instantaneous currents on fixed and voltage inductors respectively.
• $\frac{\delta M}{\delta \theta }$ is the rate of pointer deflection related to $\theta$ angle.

The restorative torque $T_{c}$ produced by the spring is:

$T_{c}=K\theta$

• $K$ is the spring constant in Newtons/meter (N/m).

When the power is being measured, the torques $T_{d}$ and $T_{c}$ are balanced and become equal.

$T_{d}=T_{c}$

$i_{c}i_{p}\frac{\delta M}{\delta \theta }=K\theta$

The deflection angle becomes:

$\theta =\frac{(i_{c}i_{p}\frac{\delta M}{\delta \theta })}{K}$

### Measurement in alternate current

Voltage value in the moving coil.

$v=V_{rms}\sqrt{2}\cdot sen(\omega t)$

If the resistance linked to voltage inductor is too high, it can be considered purely resistive. In this case,

$i_{p}=\frac{v}{R}$

$i_{p}=\frac{V_{m}\cdot sen(\omega t)}{R}$

$i_{p}=Ip_{m}\cdot sen(\omega t)$

If the current that passes through fixed inductors ($i_{c}$) is delayed in relation to $i_{p}$, the equation becomes:

$i_{p}=Ip_{m}\cdot sen(\omega t-\phi )$

While $i_{c}$:

$i_{c}=Ic_{m}\cdot sen(\omega t)$

Deflection torque equation in AC, after solving an integer.

$T_{d}=Ic_{m}Ip_{m}\cdot cos\phi \cdot \frac{\delta M}{\delta \theta }$

Deflection angle.

$\theta =\frac{Ic_{rms}Ip_{rms}}{K}\cdot cos\phi \cdot \frac{\delta M}{\delta \theta }$

### Measurement errors

The factors that cause errors in measure are: inductance and capacitance of pressure coil, mutual inductance between the coils, stray magnetic field, temperature and edgy currents.

If an electrodynamic wattmeter made for 50 Hz operates in 60 Hz, or vice-versa, edge current values will change, which can cause errors in measures.

## Induction wattmeter

This type can only be measured in AC. Consists in two electromagnets with laminated core made of steel silicon: shunt and series magnets. Between these electromagnets, there is a thin disk of  aluminum, the aluminum disk receives variable magnetic field and induced current appears on the disk. The induced current in the presence of a magnetic field produces a torque on disk, that is connected to a pointer. The copper rings on shunt magnet have adjusted position so that the generated flux and supply voltage have a phase difference of 90 degrees. Source: Tutorialspoint. The permanent magnet has the function to dampen the torque on disk. The edge current produces its own magnetic field, canceling the permanent magnet’s field. Source: Engineeringslab.

This type can only be used when the frequency, voltage and temperature are constant. However, this wattmeter can only operate in the frequency that was designed. In the other hand, Don’t suffer the effects of external magnetic fields.

### Phase diagram The quantities with “sh” are produced in the shunt electromagnet, while with “se” are related to series electromagnet. For example, E_{sh} is the induced voltage on shunt. Source: Electrical Deck.

The resulting torque $T$ is proportional to generated voltage $V$ and current $I$ and to power factor $cos\phi$.

$T_{d}\propto VI\cdot cos\phi$

## Digital wattmeter 