**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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