Electronics Fundamentals/Series Circuit/Series RL

Configuration

Z=Z_{R}+Z_{L}

Z=R+j\omega L

Z={\frac {1}{R}}(1+j\omega T)

T={\frac {L}{R}}

The Natural Response of the series RL is found by solving the 1st order Differential equation of the circuit in equilirium

L{\frac {di}{dt}}+iR=0

{\frac {di}{dt}}+i{\frac {R}{L}}=0

\int {\frac {di}{i}}=-{\frac {R}{L}}\int dt

Lni=-{\frac {t}{T}}+c

i=Ae^{(}-{\frac {t}{T}})

The Natural Response of the series RL is a Exponential Decay function of e

Total Impedance

Z=Z_{R}+Z_{L}

Z=R\angle 0+\omega L\angle 90

Z=|Z|\angle \theta

Z={\sqrt {R^{2}+(\omega L)^{2}}}\angle \omega {\frac {L}{R}}

Phase Angle Difference

Tan\theta =\omega {\frac {L}{R}}=2\pi f{\frac {L}{R}}=2\pi {\frac {1}{t}}{\frac {L}{R}}

Frequency Response

\omega =0.Z=R

\omega =0.Z={\sqrt {2}}R

\omega =oo.Z=oo

Series RL is characterised by

1st ordered Differential equation of the circuit at equilibrium.

{\frac {di}{dt}}+{\frac {1}{T}}=0

Natural Reponse of the circuit is the Exponential Decay

i=Ae^{(}-{\frac {t}{T}})

Phase shift or Frequency Change is dictated by the value of R and L

Tan\theta =\omega {\frac {L}{R}}=2\pi f{\frac {L}{R}}=2\pi {\frac {1}{t}}{\frac {L}{R}}

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