The amplitude and phase of the current in a series LCR circuit can be found with phasors. Which of the following is a drawback of this method?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → It gives only the steady-state solution and not the transient solution.
The phasor method draws the current and voltage phasors at an arbitrary instant, so it says nothing about the initial condition of the circuit.
Option (1) It gives only the steady-state solution and not the transient solution. — Correct. The amplitude and phase found from phasors describe the steady-state solution only. The general solution is the sum of this and a transient solution. The transient part exists even for \( v=0 \) and dies out after a long enough time. The phasor diagram cannot give it.
Option (2) It gives no steady-state solution. — Incorrect. The steady-state current \( i=i_m\sin(\omega t+\phi) \), with its amplitude \( i_m=v_m/Z \) and phase \( \phi \), is the result that the phasor method gives.
NCERT (2026-27):
Phasor-Diagram Solution – “… But this method of analysing ac circuits suffers from certain disadvantages. First, the phasor diagram say nothing about the initial condition. … The solution so obtained is called the steady-state solution. This is not a general solution. Additionally, 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.”