Question

A series LCR circuit is connected to an a.c. source of variable frequency. Draw a suitable phasor diagram to deduce the expressions for the amplitude of the current and phase angle.

Answer 1

The phasor diagram of series RLC circuit is drawn by combining the phasor diagram of resistor, inductor and capacitor. The current flowing in all the elements are same. For drawing the phasor diagram, take current phasor as reference and draw it on horizontal axis as shown in diagram. In case of resistor, both voltage and current are in same phase. So $V_R$ and $I$ are in same direction. In inductor, voltage leads current by ${90}^o$ so we draw $V_L$ in perpendicular to current phasor in leading direction. Similarly $V_C$ is perpendicular to current phasor in lagging direction. In resultant diagram we draw $V_C$ in upward direction. Now the resultant, $V_S$ which is vector sum of $V_R$ and $V_L{V}_C$.