Electrical Engineering ⇒ Topic : Decay of Current in an Inductive Circuit

Decay of Current in an Inductive Circuit

Consider an inductive circuit shown in Fig. (a). When switch S is thrown to position 2, the current in the circuit starts rising and attains the final value I (= r /R) after some time as explained above. If now switch is thrown to position 1, it is found that current in the R-L circuit does not cease immediately but gradually reduces to zero. Suppose at any instant, the current is i and is decreasing at the rate of di/dt. Then

                                (a)                                                                                                       (b)

Eq. (ii) gives the decay of current in an R L series circuit with time t and is represented graphically in Fig. (b). Note that decay of current follows the exponential law.

Time constant. The quantity L/R in eq. (ii) is known as time constant of the circuit. When  t=λ (= L/R),

                                                  i = Ie^-1 = 0.37 I

Hence, time constant may also be defined as the time taken by the current to fall to 0.37 of its final steady value I (= V/R) while decaying. Fig. (c) as well as adjoining table shows the percentage of initial current (I) after each time constant interval while the current is decreasing. During the first time constant interval, the current  decreases 37% of its initial value. A 5 time-constant interval is accepted as the time for the current to reduce to zero value.