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 200px Differential Equation ln V = với Time Constant t V(t) % Vo0 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 100px First Order Equation of Circuit ln I = I = I = I = Time Constant RL τ = I = A {| class="wikitable" width=50% ! 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