ENSC 320 Chapter Notes - Chapter 6: Inductor, Short Circuit, Inductance

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The inductor v-i equation: 

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If the current is constant/dc => behaves as short circuit.
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The current cannot change by a finite amount in zero time
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The inductor i-v equation:
  
-
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Energy in an inductor:  

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Section 6.1 The Inductor (Pg. 176)
The capacitor i-v equation: 

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The capacitor v-I equation:
  
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Power in a capacitor:    

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Energy in a capacitor:  
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Section 6.2 The Capacity (Pg. 182)
Inductors and capacitors are passive elements because they cannot generate/dissipate energy
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Section 6.3 Series-Parallel Combinations of Inductors and Capacitance (Pg. 187)
Combining inductors in series:        
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Combining inductors in parallel:

 
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Equivalent inductance initial current:
 
 
 
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Inductance:
Combing capacitors in series:

 
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Combining capacitors in parallel:     
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Equivalent capacitance initial voltage:
 
 
   
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Capacitance:
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& = self-inductances of the two magnetically coupled coils
Mutual inductance (M) : the pair of coils with this value of mutual inductance
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Mesh currents is used to analyze circuits containing mutual inductance (easiest way)
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"dot convention" = a method to track the polarities
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See the procedure for determining dot markings at Pg. 191
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Section 6.4 Mutual Inductance (Pg. 187)
=> = number of turns on the coil
=> Magnitude of the flux   
=> = the permeance of the space occupied by the flux
Faraday's Law:   

, where the flux linkage  [Wb]
-
 

  

;
 

 

 

 

=> For coils wound on non-magnetic cores:     
The concept of mutual inductance derived from Faraday's Law:
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=> where  and  
=> Thus, relating self-inductances and mutual inductance using coupling coefficient:
  
where = coefficient of coupling and    
=>  : the two coils have no common flux (    )
=>  : all the flux that links coil 1 also links coil 2 (    )
Mutual Inductance in terms of self-inductance
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Energy stored in magnetically-coupled coils:
 
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Section 6.5 A Closer Look at Mutual Inductance (Pg. 193)
ENSC320 Textbook Ch6 Summary
ENSC320-7 Page 1
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