# Electrical Resonance Frequency Meter

### Electrical Resonance Frequency Meter

Electrical resonance frequency meter is very simple instrument of indicating type. This instrument operates on the principle of electrical resonance, i.e. when inductive reactance (XL) and capacitive reactance (Xc) become equal, electrical resonance is said to have occurred. In this article we will study about Ferrodynamic Type Frequency Meter.

Construction

It consists of a fixed coil which is connected across the supply whose frequency is to be measured. Fixed coil is also called magnetizing coil. The magnetizing coil mounted on a laminated iron core. The iron core has a cross-section which varies gradually over the length, being maximum near the end where the magnetizing coil is mounted and minimum at the other end. The   moving coil is pivoted over this iron core. The pointer is attached to the moving coil. The capacitor is connected with moving coil. Working

When the magnetizing coil is connected across supply, the current I flows through the magnetizing coil and sets up flux Φ. If we neglect the resistance of the coil and iron losses in the core, flux Φ is phase with current I. Since flux Φ is an alternating flux, it will induce e.m.f. ‘e’ in the moving coil and current start flows.

The phase of this current depends upon the inductance L of the moving coil and the capacitance C.

The operation can be well explained with the help of phasor diagram;

In first case, the circuit of the moving coil assumed to be inductive and therefore current I lags behind the e.m.f. ‘e’ by an angle α. The deflecting torque acting on the moving coil is thus:

Td = icos(900+ α) In second case, the moving coil is assumed to be largely capacitive therefore current ‘i’ lead the e.m.f. ‘e’ by an angle β and therefore the deflecting torque is thus:

Td = icos(900 β) The torque produce in second case is opposite direction to what it was in the first case.

In third case, the inductive reactance supposed to be equal to the capacitive reactance so that i is in phase with e and the torque upon the pivoted coil is proportional to Td = icos900 which is Zero. Coming to actual operation of the instrument for a fixed frequency is constant but the inductive reactance of the moving coil is not constant. The inductive reactance depends upon the position of the pivoted coil on the core. This inductance, hence inductive reactance is maximum when the moving coil occupies a position close to the magnetizing coil and minimum when it is at other end.

The value of capacitor ‘C’ is so selected that the moving occupies a convenient position in the centre when the frequency is at its normal value. Under these conditions the inductive reactance becomes larger than the capacitive reactance. This because the inductive reactance is directly proportional to the supply frequency and capacitive reactance is inversely proportional to the frequency. Thus the circuit becomes largely inductive and, therefore, there is a torque produced. This torque tries to pull the moving coil to an equilibrium position i.e. a position where the inductive reactance should remain equal to the capacitive reactance.

If the frequency decreases below the normal, value of the capacitive reactance becomes more than the inductive reactance and hence there is a torque produced. This torque moves the coil to a position where its inductive reactance tends to become larger and thus equals capacitive reactance. Therefore, the moving coil deflects towards the magnetizing coil. 