Calling all Physics boffins, a little help if you may!

Dunks

Dunks

Dunks

Soldato
Joined
31 Oct 2004
Posts
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Location
London
Right, currently working through some electronics and I'm stumped on a reasonably easy question.

In the circuit below you are given ε1, ε2, R1, R2 and R3. Find all the branch currents using KCL and KVL. Write down the all the steps involved to analyse the circuit using KCL and KVL by drawing the following circuit with necessary items. Finally your analysis should derive explicit expressions for all the branch currents in terms of known values ε1, ε2, R1, R2 and R3.

Following (or trying) through with an example, below:

equations.JPG


Obviously you need to re-write the equations (1), (2) and (3) before putting them into matrix form then applying Cramer's rule to solve them.

I know it's pretty simple but my brain is just not working today and cannot for the life of me work out how to do it :(.

Anyone able to point me in the right direction? :o
 
Which bit are you having trouble with? The derivation of 1-3, the writing of the 3 simultaneous equations in matrix form or solving the matrix?
 
Ok, well re-write the equations 1-3 with the constant terms on the right hand side (e1,e2).

R1.I1 - R2.I2 + 0.I3 = e1 (1*)
0.I1 + R2.I2 + R3.I3 = -e2 (2*)
1.I1 + 1.I2 - 1I3 = 0 (3*)

Now you should see that the first row of the coefficient matrix times the unknowns vector (I1,I2,I3) is equal to e1. The matrix is just another way of re-writing 1*-3* in an easily intelligible way.

Does that make sense?
 
Ok, I lied. Stuck on solving the matrix now! :p

matrix.JPG


Is what it should be. I know how to arrange it all, but how it's solved I haven't a clue.
 
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