Question

Derive the expression for impedance, current and phase angle in a series LCR circuit using phasor diagram.  

Answer 1

Consider a series LCR circuit connected to an AC source 

v = v_msinωt ---- (1) 

Let i = i_msin(ωt + ϕ) ---- (2) 

be the instantaneous current through the circuit and ϕ is the phase difference between the applied voltage and the current. Voltage equation at any instant 

Its magnitude of v is the phasor sum of v_R, v_L and v_C. 

And the phasor diagram for the circuit is as shown below. The symbols in the diagram are having usual meaning.

is analogous to resistance in DC called impedance, Z.