# RL Series Circuit

## RL series circuit A.C circuit

AC series circuits differ from DC circuits. In a dc circuit, we consider resistance only, but in an ac series circuit, resistance (R), inductance (L), inductance(L), and capacitance (C) is taken into account. L and C offer opposition (XL and XC) to the flow of current in an ac circuit. The magnitude of current in an ac circuit is affected by the supply frequency because XL = 2 fL and XC = 1/2 fC are frequency-dependent. In a dc circuit, voltage and current can be added or subtracted arithmetically, but in an ac circuit, there is a phase difference of 90° between voltage across and current through L or C.

V=rms value of applied voltage

I=rms value of the circuit current

Voltage across R=VR=IR

(VR is in phase with I i.e OA represented by the phasor diagram)

voltage across L=VL=IXL

(VL leads I by 90° i.e AB represented by the phasor diagram)

Taking current as references phasor,

Applied voltage V is the phasor sum of these two drops i.e

circuit current,

## Phase angle

From phasor current, I lags behind the applied voltage V by Φ°.

Applied voltage,

As the Inductive current lags behind the applied voltage. The angle of lag(i.e Φ) is greater than 0° but less than 90°. It is determined by the ratio of inductive reactance to resistance tanΦ=XL/R. The greater the value of this ratio, the greater will be the phase angle Φ.

## Impedance

The total opposition offered to the flow of alternating current is called impedance(Z).In the series RL circuit,

## Power

Instantaneous power p=vi

is a constant part and whose average value over one cycle is the the same.

is a pulsating component and whose average value over one complete cycle is Zero.

Average power

where V and I are the rms value of voltage and current.

Alternatively,