[SOLVED] Setting Up Linear Equations Using Kirshoff's Laws
I am having a real difficult time with the first part of my assignment. I need to set up 9 linear equations from this diagram.
Using Kirshoff's laws which are:
1.) The potential drop around each closed loop in the circuit board adds up to zero.
2.) (Current conservation) The current at each node is conserved: The amount of current flowing into
the node is equal to the amount of current flowing out of the node.
More info can be found here with an example for each law but I still do not understand. Maybe someone can help :(
Edit: The equations I am setting up are to solve i and (n=1..8)
example vertex and loop equations.
For each vertex in your circuit, the incoming current must be equal to the outgoing current. So for instance,
i4 = i2+i3 means the incoming currents, i2 and i3, must sum up to the outgoing current i4. Imagine each vertex as a door - all the people entering the door must leave the door (nobody stays there). You can do that for each vertex - there are 6 of them. Another set of equations you can write down are the loop equations. Going around a loop can't raise your potential ( think of hiking around the top of a mountain - you wind up where you started. The Escher pictures try to fool you into thinking you've gone higher or lower after 1 revolution). In your circuit, you would write down: i1*r + i3*r -i2*r = 0. (I'm assuming you didn't draw in the resistors). The negative on the i2 is because the direction of the current is backwards. One of your loop equations involves the battery. Without the battery nothing will happen. The bottom loop would then give you
V - i7*r + i5*r + i1*r = 0. I count 4 loop equations in your circuit. Hope this gets you started.