Electronics Handbook/Circuits/RLC Series Analysis
Consider an RLC series circuit
- If L = 0 then the cicuit is reduced to RC series
- If C = 0 then the cicuit is reduced to RL series
- If R = 0 then the cicuit is reduced to LC series
- If R, L , C are not zero
RC Series
[edit | edit source]- Differential Equation
- ln V =
- với
- Time Constant
t | V(t) | % Vo |
---|---|---|
0 | A = eC = Vo | 100% |
.63 Vo | 60% Vo | |
Vo | ||
Vo | ||
Vo | ||
.01 Vo | 10% Vo |
- Circuit Impedance
Z/_θ
- Z = R /_0 + ( 1 / ωC ) /_ - 90
- Z = = |Z|/_θ = /_ Tan-1
Z(jω)
- Z =
- )
- Angle Difference Between Voltage and Current
There is a difference in angle Between Voltage and Current . Current leads Voltage by an angle θ
The difference in angle between Voltage and Current relates to the value of R , C and the Angular of Frequency ω which also relates to f and t . Therefore when change the value of R or C , the angle difference will be changed and so are ω , f , t
- First Order Equation of Circuit
- ln I =
- I =
- I =
- I =
- Time Constant RL
- τ =
- I = A
t I(t) % Io 0 A = eC = Io 100% .63 Io 63% Io Io Io Io .01 Io 10% Io
- Circuit Impedance
- = R/_0 + ω L/_90
- Z = |Z|/_θ = /_Tan-1
Z(jω)
- Angle of Difference Between Voltage and Current
In RL series circuit, only L is the component that depends on frequency . There is no difference between voltage and current on R . There is an angle difference between voltage and current by 90 degree . When connect R and L in series , there is a difference in angle between voltage and current from 0 to 90 degree which can be expressed as a mathematic formula below
- In Summary
RL series circuit has a first order differential equation of current
Which has one real root of the form
Which has solution in the form