[<< wikibooks] Circuit Theory/Thevenin-Norton
== Vth using Node ==

  
    
      
        
          V
          
            t
            h
          
        
        =
        6.4516
      
    
    {\displaystyle V_{th}=6.4516}
  


== In using Node ==

  
    
      
        
          I
          
            N
          
        
        =
        1.064773736
      
    
    {\displaystyle I_{N}=1.064773736}
  


== Rth or Rn ==

  
    
      
        
          V
          
            t
            h
          
        
        
          /
        
        
          I
          
            N
          
        
        =
        
          
            6.4516
            1.064773736
          
        
        =
        6.0591
        o
        h
        m
        s
      
    
    {\displaystyle V_{th}/I_{N}={\frac {6.4516}{1.064773736}}=6.0591ohms}
  


== Finding Rth using source injection and node ==

		
		
Here is the mupad/matlab code that generates the answer Rth = 6.0591 ohms.


== Comparing Node with Thevenin Equivalent ==

Solving the node equations yields:

  
    
      
        
          V
          
            a
          
        
        =
        5.393
      
    
    {\displaystyle V_{a}=5.393}
  

  
    
      
        
          V
          
            b
          
        
        =
        1.1673
      
    
    {\displaystyle V_{b}=1.1673}
  

  
    
      
        
          V
          
            c
          
        
        =
        1.107
      
    
    {\displaystyle V_{c}=1.107}
  

  
    
      
        
          i
          
            12
          
        
        =
        0.3571
      
    
    {\displaystyle i_{12}=0.3571}
  

  
    
      
        
          v
          
            12
          
        
        =
        4.286
      
    
    {\displaystyle v_{12}=4.286}
  Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:

  
    
      
        
          v
          
            12
          
        
        =
        
          V
          
            s
          
        
        ∗
        
          
            12
            
              R
              
                t
                o
                t
                a
                l
              
            
          
        
      
    
    {\displaystyle v_{12}=V_{s}*{\frac {12}{R{total}}}}
  

  
    
      
        
          v
          
            12
          
        
        =
        6.4516
        ∗
        
          
            12
            
              6.0591
              +
              12
            
          
        
        =
        4.287
      
    
    {\displaystyle v_{12}=6.4516*{\frac {12}{6.0591+12}}=4.287}
  So they match ...
Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.