✱WHAT IS TRANSIENT?
➝"Transient is occurs due to the sudden change in the supply voltage or change in energy stored by memory element (Inductor or capacitor) is called as a transient".
➝The time taken by memory element to comes from one steady state value to another steady state value is referred as a Transient time or response of an ac Circuit.
- Electrical Network or Circuit is mainly consisting of three elements, which are ;
- RESISTANCE (R)
- INDUCTOR (L)
- CAPACITOR (C)
- Out of this three elements Inductor (L) and Capacitor (C) are memory elements because it stored energy proportional to the 1/2 L×I^2 and 1/2 C×V^2 respectively, but Resistor (R) is memory less element because it doesn't stored any energy in it.
- Now we are studying standard discharging and normal discharging equation.
❋STANDARD DISCHARGING EQUATION:-
y0 (t) = y0 e^-t/τ .........(1)
Where; τ= Time constant
Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞
y (t=0) = y0 × e^-0 = y0
y (t=τ) = y0 × e^-1 =0.367 y0
y (t=2τ) = y0 × e^-2 =0.135 y0
y (t=∞) = y0 × e^-∞ =0
 |
| Fig (a) STANDARD DISCHARGING CURVE. |
➝As shown in the above figure behaviour of standard discharging.
❋NORMAL DISCHARGING EQUATION:-
y(t) = K + y0 × e^-t/τ ...........(2)
Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞
y(t=0) = K + y0 × e^-0 = K +y0
y(t=τ) = K + y0 × e^-1 = K +0.368y0
y(t=∞) = K + y0 × e^-∞ = K
Fig (b) NORMAL DISCHARGING CURVE.
- Please remember in Network Theory "t = 5τ" is called as a SETTLING TIME.
- "SETTLING TIME IS DEFINED AS A TIME AT WHICH RESPONSE OF THE NETWORK IS COMES TO STEADY STATE REGION IS CALLED AS A SETTLING TIME OF NETWORK".
- From the above discussion we conclude that Ideally the memory element (Inductor or capacitor) is DISCHARGED TO ZERO but Practically it doesn't discharge to Zero (few amount of energy is stored in it).
