# Phase Locking in Parallel RLC at Resonance Frequency

I understand the mathematics of RLC circuits at resonance frequency, but I am having some difficulty in coming to an intuitive grasp of the physics behind it.

When the reactances of the inductor and capacitor cancel at the resonance frequency, do the total voltage and current of the circuit become phase locked because the inductor and capacitor are essentially removed from the circuit, leaving only the current across the resistor which instantaneously follows the source voltage?

To clarify, when I say that the inductor and capacitor are essentially removed from the circuit, what I mean is that due to their voltages being $180^{\circ}$ out of phase and canceling each other, the current in the circuit bypasses their branches and only passes through the resistor branch.

Thank you all ahead of time for your responses.

• In RLC circuit they are in series ,there are no branches! – Utkarsh futous Apr 5 '17 at 7:00
• @Utkarshfutous There does exist a parallel LCR circuit... – Kunal Pawar Apr 5 '17 at 8:46

## 1 Answer

Your title is about a parallel LCR circuit but your text seems to be moving towards a series LCR circuit.

If you have a circuit consisting of an ideal inductor $L$ , an ideal capacitor $C$ which is charged and a switch and you close the switch then an oscillatory current flows in the circuit with first the energy within the circuit stored in the capacitor, then the inductor, then the capacitor etc.
The frequency of the oscillator current is $\omega = \frac{1}{\sqrt{LC}}$.

Now consider the inductor and capacitor as a parallel combination in series with an ac power supply set to a frequency of $\omega = \frac{1}{\sqrt{LC}}$.

In the steady state an oscillating current will circulate around the LC loop but no current will flow in the ac power supply circuit.
As far as a circuit outside the LC loop is concerned the when the current in the capacitor is going in one direction there is an equal in magnitude but opposite in phase current passing through the inductor.
The LC loop acts as an infinite impedance.
This is sometimes called a tank circuit, the "tank" having this circulating oscillator current "stored" within in it.

In practice the components are not ideal and have resistance associated with them and so the power supply does deliver some current and hence power due to the energy losses in the resistive parts of the circuit.

In the same way that at resonance in an LCR series circuit the voltages across the inductor and capacitor can be very much larger than the supply voltage in the LCR parallel circuit the currents passing through the inductor and the capacitor can be very much larger than the power supply current.

In a parallel LCR circuit it is the voltages across each of the components which are in phase whereas in a series LCR circuit it is the currents though each of the components which are in phase.

A series combination of ideal capacitor and ideal inductor have a zero impedance at resonance because the voltages across them are equal in magnitude but exactly opposite in phase.
Remember the original LC circuit that in mentioned which had no ac power supply in it.
If that circuit is considered as a series circuit it has an oscillating current passing through it an the voltages across the capacitor and inductor are equal in magnitude but exactly opposite in phase.
The ac power supply is there to supply power to a real circuit which will have resistance and the power supply compensates for the energy losses in the resistive part of the circuit.