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
From phasor current, I lags behind the applied voltage V by Φ°.
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.
The total opposition offered to the flow of alternating current is called impedance(Z).In the series RL circuit,
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.
where V and I are the rms value of voltage and current.