## Saturday, September 17, 2016

### Alternate Current through LCR circuits

Alternate current through inductor and resistors in series

Let us consider a resistor and inductor connected to end to end. We know when current is passing through a resistor, there is no phase difference generated and when the alternate current is passed through inductor, the current lags by 90 degree.

Thus the inductive reactance and resistance of the resistor are perpendicular and hence we can measure the effective voltage and effective opposition as shown in the diagram below.

When a capacitor and resistor are connected in series an alternate current is passed through the combination, the current lags by 90 degree and we can find the effective voltage and resistance can be measured as shown.

Alternate current through LCR circuit

Let us assume inductor, capacitor and resistor are connected in series. Let us assume alternate current and source is connected to the series circuit. When the current passes through the system, a phase difference of 180 degree. It is just because, both inductor and capacitor generates 90 degree and 90 degree. Thus the total of 180 degree of phase difference is generated in the circuit.

We can measure the effective EMF and effective resistance of the circuit as shown in the diagram below.

It can be understood that, together inductor, capacitor and resistor offers opposition to the flow of the current. The capacitive reactance and inductive reactance are in the opposite direction and the effective value of these two is the difference between them.

If we want the maximum current to be passed in the circuit, the total impedance of the circuit has to be minimum. That is possible when the opposition of the inductor and capacitor cancels each other.

In that case the circuit will pass maximum current through it and the circuit is said to be in resonance. This particular frequency is called resonant frequency.

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