Draw phasor diagram for `X_(C ) gt X_(L)` and `X_(C ) lt X_(L)` and give the disadvantages of this method.

Explanation

If `X_(C ) gt X_(L)" " phi` is positive and the circuit becomes capacitive, consequently the current in the circuit leads the source voltage.
If `X_(C ) lt X_(L)" " phi` is negative and the circuit becomes inductive consequently the current in the circuit lags the source voltage.
The phasor diagram and variation of V and I with `omega t` for the case `X_(C ) gt X_(L)` is shown in figure.

Thus, we have obtained amplitude and phase of current for an LCR series circuit using the technique of phasors, but in this method there are certain disadvantes.
First, the phasor diagram say nothing about the initial condition.
Second, one can take any arbitrary value of t and draw different phasors. The solution so obtained is called the steady-state solution. This is not a general solution.
Moreover, we do have a transient solution which exists even for V =0.
The general solution is the sum of the transient solution and the steady -state solution.
After a sufficiently long time, the effects of the transient solution die out and the behaviour of the circuit is described by the steady -state solution.