Electrical Engineering ⇒ Topic : Time Constant

Time Constant

Consider the eq. (ii) above showing the rise of current w.r.t. time t.

The exponent of e is Rt/L. The quantity L/R has the dimensions of time so that exponent of e (i.e. Rt/L) is a number. The quantity L/R is called the time constant of the circuit and affects the rise of current in the circuit. It is represented by λ.

Time constant of an inductive circuit can be defined in the following ways

(i) Consider the graph showing the rise of current w.r.t. time t [See Fig. (a)]. The initial rate of rise of current (i.e. at t = 0) in the circuit is

                                                              figure (a)

If this rate of rise of current were maintained, the graph would be linear [i.e. OA in Fig. (a)] instead of exponential. If this rate of rise could continue, the circuit current will reach the final value I (= V/R) in time

Hence time constant may be defined as the time required for the current to rise to its final steady value if it continued rising at its initial rate (i.e. V /L).

Hence time constant can also be defined as the time required for the current to reach 0.632 of its final steady value while rising.

Fig  (b) as well as adjoining table shows the percentage of final current (I) after each time constant interval during current buildup (i) in the inductor. The current will increase to about 63% of its full value (I) in first time constant. A 5 time-constant time interval is accepted as the time for the current to attain its final value I.

                                                                   figure (b)