# Frequency Meter (Electrical resonance type)

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Construction:

It consists of a laminated iron core light of varying cross-section, a fixed magnetizing coil mounted at one end of the iron core and a moving coil with a pointer attached to it and pivoted so that it can move freely over the iron core as shown.

The moving coil is connected across a capacitor ‘C and the fixed coil is connected across the supply circuit, whose frequency is to be measured.

Working:

When the magnetizing coil is connected across the supply circuit, current I flow through it and a flux ó in phase with current is set up is the iron core and an e.m.f ‘e’. lagging behind the flux ф by 90˚ is induced in the moving coil. The current in the moving coil is either lagging or leading the induced emf ‘e’’, which depends upon whether the moving coil is inductive or capacitive respectively. The current in the moving coil will be in phase with ‘e’ when inductance reactance (XL) is equal to capacitive reactance (XC) as shown in phasor diagram.

The torque on the moving system is given by

T ∝ Ii cos (90˚± α)

where I = Magnetizing oil current.

i = Moving coil current

α= Phase angle between current and emf induced in the moving coil

The torque on the moving system is zero when XL= Xc.  A tactual operating condition, the capacitive reactance (1/ω C =1/2πfC) is constant for any given frequency. The inductive reactance ωL (2πfL) depends upon the position of pivoted coil on the core. The nearer this coil approaches the magnetizing coil the greater is its inductance. The pivoted coil is pulled towards the magnetizing coil until ωL=1/ωC and the torque is zero at this condition, i.e. the circuit of moving coil is in resonance. The value of capacitor ‘C’ is so chosen that the pivoted coil takes up a convenient mean position when frequency is at its normal value. If the frequency increased 1/ωC decreases and the coil moves off the core, so that its inductance is reduced to the point where ωL again equals 1/ωc. The coil moves farther ‘on’ to the core if frequency falls.