Time Constant

Assalamualaikum.

In this post, I would like to tell you about TIME CONSTANT.

The Time Constant

• All Electrical or Electronic circuits or systems suffer from some form of "time-delay" between its input and output, when a signal or voltage, either continuous, ( DC ) or alternating ( AC ) is firstly applied to it. 

• This delay is generally known as the time delay or Time Constant of the circuit and it is the time response of the circuit when a step voltage or signal is firstly applied. The resultant time constant of any circuit or system will mainly depend upon the reactive components either capacitive or inductive connected to it and is a measurement of the response time with units of, Tau - τ

• When an increasing DC voltage is applied to a discharged Capacitor the capacitor draws a charging current and "charges up", and when the voltage is reduced, the capacitor discharges in the opposite direction. Because capacitors are able to store electrical energy they act like small batteries and can store or release the energy as required.

• The charge on the plates of the capacitor is given as: Q = CV. This charging (storage) and discharging (release) of a capacitors energy is never instant but takes a certain amount of time to occur with the time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value being known as its Time Constant ( τ ).

• So mathematically we can say that the time required for a capacitor to charge up to one time constant is given as:
  
  Where, R is in Ω's and C in Farads.
  
  
  
  
  Now, I will show you an example that I obtain from internet. It is just a simple example for your further understanding. 
  
  
  
  
  
  
  
  
  
  

  Calculate the time constant of the following circuit.
  	The time constant τ is found using the formula T = R x C in seconds. Therefore the time constant τ is: T = R x C = 47k x 1000uF = 47 Secs
  a) What value will be the voltage across the capacitor at 0.7 time constants?
  At 0.7 time constants ( 0.7T ) Vc = 0.5Vs. Therefore, Vc = 0.5 x 5V = 2.5V
  b) What value will be the voltage across the capacitor at 1 time constant?
  At 1 time constant ( 1T ) Vc = 0.63Vs. Therefore, Vc = 0.63 x 5V = 3.15V
  c) How long will it take to "fully charge" the capacitor?
  The capacitor will be fully charged at 5 time constants.         1 time constant ( 1T ) = 47 seconds, (from above). Therefore, 5T = 5 x 47 = 235 secs That's all from me. Before I end up my post, I would like to share a few quotes to all of my comrades.

  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
                                                                                            Written by : Quraisya