Electronics Handbook/Circuits/Parallel Circuit

Series Circuit

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Electronic components R,L,C can be connected in parallel to form RL, RC, LC, RLC series circuit

  1. RC Parallel
  2. RL Parallel
  3. LC Parallel
  4. RLC Parallel

Parallel RC

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The total Impedance of the circuit

 
 )
T = RC

At Equilibrium sum of all voltages equal zero

 
 
 
 
ln V =  
 
 
 
T = RC

Circuit's Impedance in Polar coordinate

 
 
 

Phase Angle Difference Between Voltage and Current There is a difference in angle Between Voltage and Current . Current leads Voltage by an angle θ

 


Summary

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RL series circuit has a first order differential equation of voltage

 

Which has one real root

 
 

The Natural Response of the circuit at equilibrium is a Exponential Decrease function

Phase Angle Difference Between Voltage and Current

 

Parallel RL

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The total Circuit's Impedance In Rectangular Coordinate

 
 
 

At Equilibrium sum of all voltages equal zero

 
 
 
ln I =  
I =  
I =  
I =  


Circuit's Impedance In Polar Coordinate

 
 


Phase Angle of Difference Between Voltage and Current

 

Summary

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In summary RL series circuit has a first order differential equation of current

 

Which has one real root

 
 

The Natural Response of the circuit at equilibrium is a Exponential Decrease function

Phase Angle of Difference Between Voltage and Current

 

Parallel LC

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Natural Response

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The Total Circuit's Impedance in Rectangular Form

 
  . ZL = ZC
  . ZL = ZC

Circuit's Natural Response at equilibrium

 
 
 
 
 
 
 

The Natural Response at equilibrium of the circuit is a Sinusoidal Wave

Resonance Response

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At Resonance, The total Circuit's impedance is zero and the total volages are zero

 
 
 
 
 

The Resonance Reponse of the circuit at resonance is a Standing (Sinusoidal) Wave

Parallel RLC

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Natural Response

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At Equilibrium, the sum of all voltages equal to zero

 
 
 
 
 

Với

 
 
 

Khi  

 
 
The response of the circuit is an Exponential Deacy


Khi  

 
 
The response of the circuit is an Exponential Deacy


Khi  

 
 
The response of the circuit is an Exponential decay sinusoidal wave


Điện Kháng Tổng Mạch Điện

 
 
 

Resonance Response

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The total impedance of the circuit

 
 
 
 
 

At resonance frequency   the total impedance of the circuit is Z = R ; at its minimum value and current will be at its maximum value  :  

Look at the circuit, at   , Capacitor opens circuit . Therefore, current is equal to zero . At   , Inductor opens circuit . Therefore, current is equal to zero

Summary

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Series RL, RC

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Series RC and RL has a Character first order differential equation of the form

 

that has Decay exponential function as Natural Response

 
f(t) = i(t) for series RL
f(t) = v(t) for series RC

Series LC, RLC

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Series LC and RLC has a Characteristic Second order differential equation of the form

 
 
 

At equilibrium , the Natural Response of the circuit is Sinusoidal Wave

 

At Equilibrum , the Resonance Response is Standing Wave Reponse