Electrical Engineering ⇒ Topic : Time Constant

Time Constant

Consider the eq. (iii) above showing the rise of voltage across the capacitor.

The exponent of e is t/RC. The quantity RC has the *dimensions of time so that exponent of e is a number. The quantity RC in called the time constant of the circuit and affects the charging (or discharging) time. It is represented by λ (or T or T).

                                  Time constant, λ = RC seconds

Time constant may be defined in one of the following ways

(i) At the instant of closing the switch, p.d. across capacitor is zero. Therefore, putting v = 0 in the expression 

If this rate of rise of voltage could continue, the capacitor voltage will reach the final value r 'in time = V divide V/CR = RC seconds = time constant λ .

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

(2) If the time interval t = λ  (or RC), then

Hence time constant can also be defined as the time required for the capacitor voltage to reach 0.632 of its final steady value V.

(3) If the time interval t = λ   (or RC), then,

Hence time constant can also be defined as the time required for the charging current to fall to 0.37 of its initial maximum value In,

Fig. (a) as well as adjoining table shows the percentage of final voltage (V) after each time constant interval during voltage buildup (v) across the capacitor. An uncharged capacitor charges to about 63% of its fully charged voltage (V) in first time constant. A 5 time-constant interval is accepted as the time to fully charge (or discharge) a capacitor and is called the transient time.

                                                                         figure (a)