In this article, we shall study resonating circuit: a) LCR Series Circuit and b) LC parallel circuit.

Series Resonating Circuit:

Consider LCR circuit containing Resistance R, Inductance L and capacitance C connected in series. Let the combination be connected to an A.C. source supplying current i = i_o Sinωt.

The instantaneous e.m.f. of the circuit is equal to the sum of voltage drops across the resistor, the capacitor, and the inductor.

Dividing both sides of the equation by C

Substituting the values of equations (2) and (3) in equation (1)

Substituting these values in equation (4) we have

Thus the e.m.f. leads the current in phase  given by

In this condition the impedance of the circuit is minimum and the circuit acts as a purely resistive circuit. The current in the circuit is maximum. This condition is called a series resonance of the circuit. At resonance

The frequency f_r is called the resonating frequency. The frequency at which the resonance takes place and the maximum current flows through the circuit is called the resonating frequency.

The variation of the current with frequency for the series LCR circuit is as shown in the graph.

Parallel Resonating Circuit:

 Consider LC circuit containing Inductance L and capacitance C connected in parallel. Let the combination be connected to an A.C. source with e.m.f.  e = e_o Sin ωt.

The current in the inductance lags behind the e.m.f. by π/ 2. Thus the current through the inductance is given by

Where,  X_L = Inductive reactance

The current in the capacitance leads the e.m.f. by π/ 2. Thus the current through the inductance is given by

Where X_C = Capacitive reactance

The total current in the circuit is given by

When X_L = X_C i.e. ωC =  1/ ωL , the current in the circuit is zero. This condition is called parallel resonance of the circuit.

At resonance

The frequency f_r is called the resonating frequency. The frequency at which the resonance takes place and the zero current flows through the circuit is called the resonating frequency. At resonating frequency the impedance is maximum.

Science > Physics > Electromagnetic Induction > Resonating Circuit

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