# Dynamometer type single-phase power factor meter

Construction:

It consists of a fixed coil FF (split into two parts) which carries the current of the circuit under test. So, the magnetic field produced by this coil is proportional to the main current.

The identical pressure coils A and B pivoted on a spindle constitutes the moving system. Pressure coil A has a non-inductive resistance R which is connected in series with it, and coil B has a highly inductive choke coil L which is connected in series with it. The two coils are connected across the voltage of circuit. The value of R and L are so adjusted that the two coils carry the same value of current at normal frequency i.e. R= WL.

The current through the coil A is in phase with the circuit voltage while that through the coil B legs the voltage by an angle ẟ which is nearly equal to 90°. The angle between the planes of coils is equal to δ. Connections to moving coils are made through thin silver or gold ligaments which are extremely flexible and this gives a minimum control effect on the moving system.

Theory :

Let the current through coil B lags the voltage by exactly 90˚.

The field of the two fixed coils is uniform and in the direction of arrow. The torque on each coil for a given coil current will be maximum when the coil is parallel to the filed. i.e. along XX. When the system power factor angle is φ, the coils take up a position of equilibrium displaced θ from the vertical. Then the torque due to the two coils must be equal and opposite. Now since the current in coil A is in phase with the system voltage, the field in which it moves is proportional to the system current, then coil A is essentially a wattmeter movement displaced 90˚- θ from the maximum torque position. Then the torque of A is given by

TA=KVI cos φ cos (90˚- θ)

where k is a constant.

Similarly, since the current in coil B lags 90° on the system voltage, coil B is in a sine meter movement displaced θ from the maximum torque position. Then torque on B is.

TB = KVI sin φ cos θ

Hence at equilibrium TA = TB

i.e. KVI cos φ cos (90˚- θ) KVI sin φ cos θ

or,          sin φ cos θ = cos φ sin θ

or,          tan θ = tan φ      or,          θ = φ

therefore, the deflection of the instrument is a phase angle of the circuit.

Also Read- Polar type AC potentiometer