Electronics Handbook/Circuits/RL Series

Series RL Circuit

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Circuit Analysis

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Circuit Impedance

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In Polar Coordinate

  = R/_0 + ω L/_90
Z = |Z|/_θ =  /_Tan-1 

In Rectangular Coordinate

 
 

Phase Angle of Difference Between Voltage and Current

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In RL series circuit, only L is the component that depends on frequency . There is no difference between voltage and current on R . There is an angle difference between voltage and current by 90 degree . When connect R and L in series , there is a difference in angle between voltage and current from 0 to 90 degree which can be expressed as a mathematic formula below

 
 
 
 


Natural Response

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ln I =  
I =  
I =  
I =  

Time Constant RL

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τ =  
I = A  
t I(t) % Io
0 A = eC = Io 100%
  .63 Io 63% Io
  Io
  Io
  Io
  .01 Io 10% Io

Current of the circuit is decreased exponentially with time . At time t = 0 I = Io . At time t = R/L I = 63% Io . At time t = 5 time time constant I = 10% Io

I = A  

Summary

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

 

Which has one real root