# RLC Series Circuit

## RLC Series Circuit

The RLC Series Circuit is a circuit that consists of a  pure resistance of R ohms, a pure inductance of L Henry, and a pure capacitance of C farads connected together in series in combination with each other.

The voltage across R, VR=IR    where VR is in phase with I.

voltage across C, Vc=IXc   where Vc lags I by 90°.

In the phasor diagram OA represents VR, AB represents VL and AC represents VC. It is seen that VL is in phase opposition to VC. It follows that the circuit can either be effectively inductive or capacitive depending upon which voltage (VL or VC) is pre-dominant.

For the case considered, VL>VC so that the net voltage drop across the L-C combination is (VL-VC )and is represented by AD.

Therefore, the applied voltage V is the phasor sum of VR and  VL-VC and is represented by OD.

### Circuit power factor

since XL, XC, and R are known and the phase angle Φ of the circuit can be determined.

## Three cases of RLC Series circuits

### Case 1

1. When XL-XC is positive(i.e XL>XC), phase angle Φ is positive and the circuit will be inductive. In other words, in such case, the circuit current I will lag behind the applied voltage V by Φ, the value of Φ being given by tanΦ.

### Case 2

2. When XL-XC is negative(i.e XC>XL) phase angle Φ is negative and the circuit is capacitive. In such case the circuit current I leads the applied voltage V by Φ, the value of Φ being given by tanΦ.

### Case 3

3. When XL-XC is Zero(XL=XC) ,the circuit is purely resistive. In other words, circuit current I and applied voltage V will be in phase i.e Φ=0. The circuit will then have a unity power factor.

If the equation for the applied voltage V=Vm sinwt , then equation for the circuit current will be

The value of Φ will be positive or negative depending upon which reactance (Xl or XC) predominates.