Time Constant

Thursday, 23 August 2018

12:46 PM

Machine generated alternative text: Time constant • The speed at which the voltage decays depends on the coefficient of t in the power of exponential function, which can be expressed in terms of the time constant. The time constant of a circuit is the time required for the response to decay to l/e (or 36.8%) of its initial value or to increase to 1 — l/e (or 63.2%) of its final value. It is denoted by T. • This implies that at t = T, the voltage should be 0.368%: = Voe 0.368 vo o -1 = 0.368% * T = RC v(t) r = Voe¯7T = Voe¯F

 

Machine generated alternative text: • For every time interval of T, the voltage is reduced to 36.8 percent of its previous value. — A circuit with a small time constant has a fast response and vice versa. • After 5 time constants, the voltage v(t) on the capacitor is less that one percent of its initial value Vo. It takes 5t for an RC circuit to reach its final state or steady-state (either fully charged or fully discharged). r = 0.5 2 3 4 5 v(t) 0.36788 0.13534 0.04974 0.01832 0.00674

 

 

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