Electronics/Electronics Formulas/Series Circuits/Series RL

Circuit Configuration

The total Impedance of the circuit

Z=Z_{R}+Z_{L}

Z=R+j\omega L

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

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

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

The root of the equation is a Exponential Decay function chracterised the Natural Response of the circuit

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

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 Shift , Change in Frequency relate to change in RL value

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

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}})

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