[Graphics:Images/KirchoffMod_gr_49.gif]

Solution 4.

Set up the equations.

[Graphics:../Images/KirchoffMod_gr_81.gif]


[Graphics:../Images/KirchoffMod_gr_82.gif]

[Graphics:../Images/KirchoffMod_gr_83.gif]

Make the substitutions for the resistors and batteries.  

[Graphics:../Images/KirchoffMod_gr_84.gif]


[Graphics:../Images/KirchoffMod_gr_85.gif]

[Graphics:../Images/KirchoffMod_gr_86.gif]

[Graphics:../Images/KirchoffMod_gr_87.gif]

[Graphics:../Images/KirchoffMod_gr_88.gif]

We are done.

Aside.  The solution could be found using Cramer's rule.

[Graphics:../Images/KirchoffMod_gr_89.gif]



[Graphics:../Images/KirchoffMod_gr_90.gif]

[Graphics:../Images/KirchoffMod_gr_91.gif]

[Graphics:../Images/KirchoffMod_gr_92.gif]

[Graphics:../Images/KirchoffMod_gr_93.gif]

[Graphics:../Images/KirchoffMod_gr_94.gif]


[Graphics:../Images/KirchoffMod_gr_95.gif]


[Graphics:../Images/KirchoffMod_gr_96.gif]

[Graphics:../Images/KirchoffMod_gr_97.gif]

[Graphics:../Images/KirchoffMod_gr_98.gif]

[Graphics:../Images/KirchoffMod_gr_99.gif]


[Graphics:../Images/KirchoffMod_gr_100.gif]

[Graphics:../Images/KirchoffMod_gr_101.gif]

[Graphics:../Images/KirchoffMod_gr_102.gif]


[Graphics:../Images/KirchoffMod_gr_103.gif]


[Graphics:../Images/KirchoffMod_gr_104.gif]

[Graphics:../Images/KirchoffMod_gr_105.gif]

[Graphics:../Images/KirchoffMod_gr_106.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004