Using Kirchhoff\'s Laws I have to come up with three equations based on a combin

Question

Using Kirchhoff's Laws I have to come up with three equations based on a combination circuit that can be used to predict the current in each branch of a circuit. Two of the equations should be derived from the loop rule, and the third from the junction rule. I am posting the relevant materials below in images.

The three equations should be in the form:

I1=

I2=

I3=

Thanks for your help!!

In case CHEGG deletes the above images like they absolutely love to do, here is a link:

http://imgur.com/6iMh6

http://imgur.com/4Rb3w

Click EDIT -> Rotate ( if needed).

Explanation / Answer

Our first equation will come from the Junction Rule: (We will use the junction at the top of the circuit) The junction rule states: the current entering a junction must equal the current that is leaving a junction. Using this definition, we get the following equation: I1 = 12 + I3 Our next two equations will come from the Loop Rule: (We will use the left loop and the right loop; though we could also use the entire loop if we so choose) The loop rule states: the total voltage throughout any loop must sum to zero L1: Va - (R1)(I1) - (R3)(I3) = 0 Va = (R1)(I1) + (R3)(I3) L2: -(R2)(I2) - Vb + (R3)(I3) = 0 Vb = -R2(I2) + (R3)(I3) So to summarize: EQN1: I1 - I2 - I3 = 0 EQN2: (R1)(I1) + 0(I2) + (R3)(I3) = Va EQN3: 0(I1) - (R2)(I2) + (R3)(I3) = Vb now if you have the values, you can plug them in and using a system of equations or a matrix to solve for the three values of I. BOL

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