### How to connect LCR circuit in series combination

**LCR circuit:** Suppose a resistance R. an inductance L and a capacitance C are connected in series to a source of alternating emf

Where emf of alternating current

Let I be the current in the series circuit at any instant. Then voltage will be differ due to R, L and C.

Potential across resistor: R will be in same phase with

Potential across inductance coil Inductance L is ahead of current by

potential across capacitor Capacitance C lags behind the current by

Where R = Resistance I = current

As and are in opposite direction their resultant will be

The resultant of and must be equal to the applied emf

So using Pythagorean Theorem, we get

The effective resistance of series LCR circuit which opposes the flow of current is called Impedance. It is denoted by Z.

**Special cases:**

**(i)** **Inductive LCR circuit**

The emf is ahead of current by angle

**(ii) Capacitive LCR circuit**

The current is ahead of emf by angle

Clearly the circuit is purely resistive

The current and voltage are in same phase and the current is maximum. This is Resonance condition

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