Expert: John Penton - 10/12/2002

Question
this is a sort of post a level question.  there is a circuit with a diamond of resistors (R1-5) and one in the centre: a bit like a triangle and its reflection in x axis

_______________
     i        |                 R1 = 10
             / \                r2 = 10
            /   \               R3 = 10
        R1 /     \ R2           R4 = 10
          /_______\             R5 = 22
          \  R3   /
           \     /           emf = 10v clockwise
        R4  \   /  R5        
             \ /
              |
_______________|      
              
find the current i

if you can help i will be grateful

Cheers

Answer
You are correct in thinking that you need Kirchoff's Law
The way I would do it is this:
(Conventions: I2 = current through R2, Va = voltage across R4, Vb = voltage across R5, V = 10V).
Use Ohm's Law on each resistor:
(V-Va) = R1.I1
Va = R4.I4
etc.
Use Kirchoff's Current Law at each junction:
I1 = I3 + I4
I2 + I3 = I5
i = I1 + I2
etc.
Solve the resulting equations for i.  This is merely an exercise in maths - which I have yet to find time to complete, it gets a little complex.  Sorry.

Alternatively, you could use Kirchoff's Voltage Law, like this:
http://www.phys.ualberta.ca/~gingrich/phys395/notes/node15.html

Or Thevanin's Theorem, like this:
http://www.broadcast.net/hallikainen/theory6.html