Solve Kirchoff's Laws: 8V, 4V, 110Ω, 40Ω, 50Ω

[shigg927]

[SOLVED] Kirchoff's Laws

Homework Statement

"The circuit in the figure is composed of two batteries (ε1 = 8 V and ε2 = 4 V) and four resistors (R1 = 110 Ω, R2 = 40 Ω, R3 = 50 Ω, and R4 = 50 Ω) as shown. What is the current I1 which flows through R1? What is the current that flows through R3?"

Homework Equations

So, I wasn't sure if the junction rule applies here, and if there is supposed to I2 that I draw in? So, my first attempt included I3=I1+I2, but it became really complicated to solve and it was still not the right answer.

The Attempt at a Solution

My second attempt included the equations 8 + 50I3 + 4 - 40I3 + 110 I1=0 for the first loop and -4 + 50 I3 -40I1=0 for the second loop. Obviously this was wrong as when I submitted, I got a big fat no. I'm so lost as to what I'm doing wrong or how to set this up, help!

 

[Bob Loblaw]

The junction rule is used here and you applied it correctly.

Start at the positive end of the battery (the longer bar) of the 8v source. The perimeter loop should give you:

8v-110I1-50I3-50I1
The left hand loop gave me:
4v-40I2-51I3.

Remember when you cross a resistor in the direction of the current, you are subtracting IR.

Combine like terms of those two equations, then use substitute for one of the variables using the junction rule.