- #1

Knissp

- 75

- 0

**[SOLVED] Kirchoff's Laws**

## Homework Statement

A link to the problem statement is provided here: http://img231.imageshack.us/img231/5305/kirchoffry1.png

(with one modification: the question should read find the current in the .75 ohm resistor)

## Homework Equations

Ohm's Law: R=delta(V)/I

loop rule: sum(changes in potentials) = 0 (for closed loop)

junction rule: because of conservation of charge, the currents follow such that:

I_1 + I_2 = I_3

## The Attempt at a Solution

I am supposed to solve a set of simultaneous linear equations. The first one is simply the node equation

I_1+I_2=I_3.

Then by looking at the top loop, I have:

2.25 - (I_2)*(3) - (I_3) * (4.2) = 0

The next part is what I am somewhat confused about.

I can either make one of two loops for the final equations: the bottom one with the middle wire included, or the top and bottom one as a whole.

For just the bottom loop, I get:

4.75 - (I_1)*(.75) + 1 - (I_1)*(1.2) + (I_2)*(3) +2.25 = 0

I am not sure if this is right because I don't know if it is appropriate to add the voltages 1 and 4.75 when they have the resistor between them. Perhaps I am supposed to use their potential difference? But then in that case, the .75 ohms would be internal resistance and I don't have any emf. And, I think it is probably incorrect to assume that the current going through the 1.2 ohm resistor is the same as I_1.

For the whole loop (the biggest one which does not include the middle wire), I get:

4.75 - (I_1)*(.75) + 1 - (I_1)*(1.2) - (I_3)*(4.2) = 0

When I solve this simultaneously with the first two equations, I get a different answer from when I solve the first three simultaneously.

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