AC Source

The current response remains unchanged when the voltage source is dc. This however is not the case when the circuit is excited by an ac source. Let us assume that the source voltage is now given by

(6.5)

where α is the phase angle of the applied voltage. We shall show that the system response changes with a change in α .

The solution of (6.2) for the source voltage given in (6.5) is

	(6.6)
A	(6.7)
A	(6.8)

,

The system response for V _m = 100 V and α = 45° is shown in Fig. 6.3. In this figure both i_ac and i _dc are also shown. It can be seen that i_ac is the steady state waveform of the circuit, while i_dc dies out once the initial transient phase is over. Fig. 6.4 shows the response of the current for different values of a . Since the current is almost inductive, it can be seen that the transient is minimum when α = 90° , i.e., the circuit is switched on almost at the zero-crossing of the current. On the other hand, the transient is maximum when α = 0° , i.e., almost at the peak of the current.

Fig 6.3 Transient in current and its ac and dc components at the instant of switch closing

Fig 6.4 Transient in current for different values of α