couple of questions in Electrical and Electronics principles

Question

David · Accepted Answer

Solution1: 
Applying node analysis at X 
      
  
 
  
  
 
(     )
  
   
Applying node analysis at X
  

  
 
(     )
  
   
For condition that no current flows through ZE
  

  
 
(     )
  

  

  
   
Equation 1:
  

  

  

  
 
(     )
  

  

  
   
Equation 2:
  

  

Dividing equation 1 and 2: 
(
      
  
)
      
  
 
 
  
  
 
  

  
  
 
  

Hence the condition for which no current passes through ZE is: 
  
  
 
  

Solution 2: 
Figure is to be converted from T model to Π model 
Given:
             ……………..equation 1 
              ……………..equation 2
From equation 1 we get:
  

 
     ………………..equation 3 
From equation 2:
  

 
     ………………..equation 4 
Results from equation 3 and 4 
  
  
 
 
 
   
  
  
 
 
 
   
  
  
 
  
  
 ( 
 
 

 
)    
  
  
 
  
  
 ( 
 
 
)    
    
 
  

  
   
Putting    in equation 3: 
  
  
 
 
 
(
  

  
  )     
  
  
 
   
   
 
 
  
      
   
   
 
 
  
      
   
   
  
 
 
  
   
Hence there are two equation we have: 
   
   
  
 
 
  
   
    
 
  

  

Converting  Y to Π:

couple of questions in Electrical and Electronics principles

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