02. RLC in Series

Impedance is a complex resistor-like term.

Resistor

U=R⋅I

Or with the complex impedance Z (a complex number):

U=Z⋅I

where:

Z:=R

Capacitor

Q=C⋅U
I=C⋅{\dot U}

When we let U and I be:

U:=U_0⋅e^{φ_u}⋅e^{j⋅ω⋅t}
{\dot U}=U_0⋅e^{φ_u}⋅j⋅ω⋅e^{j⋅ω⋅t}
I:=I_0⋅e^{φ_i}⋅e^{j⋅ω⋅t}
I_0⋅e^{φ_i}⋅e^{j⋅ω⋅t}=C⋅j⋅ω⋅U_0⋅e^{φ_u}⋅e^{j⋅ω⋅t}
I=C⋅j⋅ω⋅U
÷{I}{C⋅j⋅ω}=U

or nicer:

U=Z⋅I

where:

Z:=÷{1}{j⋅ω⋅C}

Inductor coil

Induction and magnetic flux Φ:

L:=÷{dΦ}{dI}

then the self-induced voltage is:

U=L⋅÷{dI}{dt}

When we let U and I be:

U:=U_0⋅e^{φ_u}⋅e^{j⋅ω⋅t}
I:=I_0⋅e^{φ_i}⋅e^{j⋅ω⋅t}
{\dot I}=÷{dI}{dt}=j⋅ω⋅I_0⋅e^{φ_i}⋅e^{j⋅ω⋅t}

Then:

U_0⋅e^{φ_u}⋅e^{j⋅ω⋅t}=L⋅j⋅ω⋅I_0⋅e^{φ_i}⋅e^{j⋅ω⋅t}
U=j⋅ω⋅L⋅I

or nicer:

U=Z⋅I

where:

Z:=j⋅ω⋅L

Author: Danny (remove the ".nospam" to send)

Last modification on: Thu, 09 May 2013 .