Study of dc transients and steady state response of a series R-L circuit.

Ideal Inductor: Fig. shows an ideal inductor, like an ideal voltage source, has no resistance and it is excited by a dc voltage source

An ideal inductor connected to a constant voltage source

The switch ‘ S ’ is closed at time ‘t = 0 ’ and assumed that the initial current flowing through the ideal inductor i(0)  just before closing the switch is equal to zero. To find the system response  one can apply KVL around the closed path.

Above Equation implies that the current through inductor increases with increase in time and theoretically it approaches to infinity as t → ∞ but in practice, this is not really the case.

Real or Practical inductor:

Below Fig shows a real or practical inductor has some resistance and it is exactly equal to the resistance of the wire used to wind the coil.

                                  Representation of a practical inductor

Let us consider a practical inductor is connected in series with an external resistance  and this circuit is excited with a dc voltage  as shown in fig.

(a) A practical inductor connected to a constant voltage source

(b) Equivalent representation circuit

Our problem is to study the growth of current in the circuit through two stages, namely; (i) dc transient response (ii) steady state response of the system.