Electronics/RC transient

For a series RC consist of one resistor connected with one capacitor in a closed loop.

Circuit ImpedanceEdit

In Polar Form Z/_θ

 
 


In Complex Form Z(jω)

 
T = RC

Differential Equation of circuit at equilibriumEdit

 
 
 
 
 
 
 

Time ConstantEdit

T = R C
t V(t) % Vo
0 A = eC = Vo 100%
1/RC .63 Vo 60% Vo
2/RC Vo
3/RC Vo
4/RC Vo
5/RC .01 Vo 10% Vo


 

Angle Difference Between Voltage and CurrentEdit

Current leads Voltage on an angle; Does this mean in measuring a angle of DC current causes a decrease in current? Let us take some time to understand the previous math in determing a factor of sinuous solution.

 

Change the value of R and C will change the value of Angle Difference, Angular Frequency, Frequency and Time

 
 
 

u

ApplicationEdit

 

When the switch is open, the initial voltage across the capacitor is zero. When the switch closes (which we will refer to as time zero) the capacitor charges via the resistor to  .

When the switch is closed, the circuit must follow the relationship:

 
 

which is derived by analysing the circuit using Kirchoff's Voltage Law.

By letting   and rearranging the equation:

 

This is a first order linear differential equation with integrating factor:

 
 


Multiplying both sides by the integrating factor:

 

Note that:

 

Substituting and integrating both sides:

 

where K is the integration constant.

When t=0

 

Therefore:

 

When t>0 this gives:

 
 
 

when t<0: