Practical Electronics/Series RLC

A circuit of 3 components connected in series

Circuit's response

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Equilibrium Response

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At Equilibrium, the sum of all voltages equal to zero

 
 
 

The equation above can be written as below

 


With

 
 
 
 

Roots of 2nd ordered differential equation above

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Resonance Response

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The total impedance of the circuit

 
 
 
 
 
 
At   the total impedance of the circuit is Z = R . Therefore, current is equal to  
At   , Capacitor opens circuit . Therefore, current is equal to zero
At   , Inductor opens circuit . Therefore, current is equal to zero