The electrical resonance type frequency meter is an indicating type instrument. As the name suggests its action depends upon the electrical resonance.

## Construction of Electrical Resonance Type Frequency Meter

It mainly consists of a fixed coil and a moving coil. There is a laminated iron core of varying cross-section.

This varying laminated core holds the fixed coil at its one end. Then we connect this fixed coil across the supply mains.

The electrical resonance type frequency meter measures the frequency of these supply mains. Now there is a moving coil which is so pivoted at its top end that it can move along the extended core of the fixed coil like a pendulum. The pointer of the instrument is so attached at the top end of the moving coil that its tip moves along the semicircular dial. Now, we connect on a capacitor across the two leads of the moving coil.

### Working Principle of Electrical Resonance Type Frequency Meter

Due to the current in the moving coil, the moving coil produces a flux in phase with the current. This flux flows along with the extended core of the fixed coil. Therefore the flux links the moving coil. Hence, the flux induces an emf across the moving coil. Obviously, this induced emf lags the flux by 90°. Since it is a coil; the moving coil will have some inductive reactance. Again, as it is connected across a capacitor, it will have some capacitive reactance also.

### Torque Equation

Let us consider I_{1} is the supply current of the fixed coil and I_{2} is the induced current of the moving coil. Now, we have already mentioned that the phase angle between the supply current I_{1} (current in the fixed coil) and the emf induced in the moving coil is 90°. Again there is a phase difference between the induced emf and the induced current I_{2} (current in the moving coil). Let us consider the angle of this phase difference is α. So, the actual phase difference between I_{1} and I_{2} will be (90°-α). Therefore, we can write the expression of the torque (T) as

From the above expression of the torque, we can see that the torque will be zero when α is zero. That means there must not be any phase difference between the induced current and the induced emf in the moving coil.

#### Resonance

That can only be possible when inductive reactance of the moving coil becomes equal to its capacitive reactance.

Again the inductive reactance (2πfL) depends upon the angular position of the moving coil on the extended core of the fixed coil.

So, when we just switch on the supply, the fixed coil starts attracting the moving coil towards it. This attraction due to the torque acting on the moving system. Therefore, the moving coil starts rotating along with the pointer attached to it. As a result, the inductive reactance of the moving coils changes. Then after certain angular rotation of the moving coil the inductive reactance of this coil exactly becomes equal to the capacitive reactance of the coil. At that point of time, there will be no torque acting on the moving system of the electrical resonance type frequency meter. Therefore the pointer of the instrument becomes stationary at that point. If somehow the supply frequency changes, the value of inductive reactance of the instrument also changes. Therefore the resonance of the circuit gets disturbed. Therefore again the deflecting torque appears on the moving system and tries to rotate it further. Hence, again the inductive reactance of the moving coils changes. And after a certain rotation again resonance occurs. So, here again, the torque becomes zero. Therefore the pointer rests on a new position.

So, we have seen how the position of the pointer on the dial of electrical resonance type frequency meter changes with changing the supply frequency.

#### Calibration

First, we supply an electrical signal of exactly 50Hz to the moving coil. Then we find the exact position of the pointer tip on the dial and make it as 50Hz.

Then we slowly increase the supply frequency step by step and see the position at each of the steps. And we mark these positions of the pointer on the dial with the corresponding supply frequencies.

Then we reduce the supply frequency step by step and mark the corresponding positions of the pointer on the dial with corresponding frequencies.

#### Measurement of Frequency

When we connect the leads of the fixed coil of an electrical resonance type frequency meter with supply mains the position of the pointer on the dial indicates the actual frequency of the supply signal.

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