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Scott.P
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Homework Statement
This is a question from my problem set on DC circuits:
30) Determine the magnitudes and directions of the currents through each resistor. The batteries have emfs of E1 = 9.0V and E2 = 12.0V, and the resistors have values of R1 = 15Ω, R2 = 20Ω, and R3 = 30Ω.
Homework Equations
Kirchhoff two circuit laws:
Loop Rule - [itex]\Sigma[/itex] Changes in voltage around closed loop = 0
Junction Rule -> For any junction in a circuit, the current entering must equal the current leaving the junction
Ohm's law - V = IR
The Attempt at a Solution
Go around the top loop, use the loop rule. Assume current goes clockwise for both loops. Define I1 to be the current through R1, I2 to be the current through R2, and I3 to be the current through R3:
9.0V - (15Ω)(I1) - (20Ω)(I2) = 0
Go around the bottom loop, with the same assumptions as stated:
12.0V - (30Ω)(I3) - (20Ω)(I2) = 0
And, from the junction rule,
I2 = I1 + I3
So, it appears we have three variables and three equations. Just solve the system of equations right? While it may look simple, I've been struggling to solve the system for the past hour, going through several sheets of paper. I don't know what it is, if I am missing something or if I made an error forming my equations. I am currently taking T3's for a fractured patella, but I don't think they have that much of an effect on my cognitive ability. Any help?
-Scott