# Electronics/Electronics Formulas/Series Circuits/Series RL

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## Circuit Configuration[edit]

## Formula[edit]

The total Impedance of the circuit

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle Z = Z_R + Z_L}****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle Z = R + j\omega L}****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle Z = \frac{1}{R} (1 + j\omega T)}**

The 1st order Differential equation of the circuit in equilirium

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle L \frac{di}{dt} + i R = 0}**

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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle Z = Z_R + Z_L}**

Phase Shift , Change in Frequency relate to change in RL value

## Summary[edit]

Series RL is characterised by

1st ordered Differential equation of the circuit at equilibrium.

Natural Reponse of the circuit is the Exponential Decay

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle i = Ae^(-\frac{t}{T})}**