Steady State Analysis of Series, Parallel and Series Parallel combinations of R, L,C with Sinusoidal excitation:
R-L Series Circuit:
Consider an AC circuit with a resistance R and an inductance L connected in series as shown in the figure. The alternating voltage v is given by
v = vmsin(\(\omega t\))
The current flowing in the circuit is i. The voltage across the resistor is VR and that across the inductor is VL
VR=IR is in phase with I
VL=IXL leads current by 90 degrees
With the above information, the phasor diagram can be drawn as shown.
The current I is taken as the reference phasor. The voltage VR is in phase with I and the voltage VL leads the current by 90⁰. The resultant voltage V can be drawn as shown in the figure. From the phasor diagram we observe that the voltage leads the current by an angle Φ or in other words the current lags behind the voltage by an angle Φ.
The waveform and equations for an RL series circuit can be drawn as below.
From the phasor diagram, the expressions for the resultant voltage V and the angle Φ can be derived as follows
The impedance in an AC circuit is similar to a resistance in a DC circuit. The unit for impedance is ohms(Ω)
Phase angle:
Power Factor:
The power factor in an AC circuit is defined as the cosine of the angle between voltage and current ie., cosΦ
