Resistor capacitor and inductor circuits

RC and RL circuits

Application of RC and RL circuits:

These circuits are used in most of the devices and circuits……..

1.      It is used in electronics

2.      Communication

3.      Control system

Note:

Ø  When we apply Kirchhoff law on passive network then we then the answer will be in algebraic equations……………

Ø  If we use Kirchhoff law in RC and RL circuit then the answer will be in Differential Equations…………..

First order network:

A order circuit is characteristic by first order differential equations is called first order network

Excitation:

When the circuit is on or run is called excitation……

There are to type of excitation …

1.      When independent source is present ……

2.      When circuit is source free  (mean no external independent source is present)  

So there are four states in RC and RL analysis

Source free	RC circuit
Dc source	RC circuit
Source free	RL circuit
Dc source	RL circuit

Source free RC circuits

Source free RC circuit occurs when DC source disconnect and store energy of capacitor flow through the passive elements

This is the equivalent circuit of RC circuit in C is capacitor and R is equivalent resistance.

We find the response of the circuit when the DC source is disconnected and the decay and raise of the voltage of capacitors.

When the DC source is disconnected then at time t=0 it means the capacitor is fully charged.

t=0 then the capacitor is fully charged at that time voltage of capacitor of voltage is Vo

Energy store at that time is

 W=1/2(CV square)

 the voltage response of the circuits where A is a constant

V(t)=A exp(-t/RC)

So the circuit response of the circuit is exponential decay is called natural response

Natural Response:

                               When no external response is connected then the response of the circuit is natural response and in this case as dc course is disconnect so it is natural response of the circuit

                                                                                                                                                       

Time constant τ

How rapidly the Vo decay and raise it is called time constant

It is time required for the response of decay by the factor
  1/e =36.8% of Vo

                                                                                                                                    

Charging or discharging of capacitor:

                               5τ  is the charging or discharging time of the capacitor

                           With this time a capacitor is fully charged or discharge

for more detail view this link:
note in this link formulas may not shown so please download it so that you can see formulas

https://drive.google.com/file/d/0B8WnAMWZn9bUVVJlT1NKOUJTMlk/edit?usp=sharing