Calculating the Current in a Two battery Combination Circuit

[BornSurvivor]

Homework Statement

For the circuit shown in the figure below, calculate the current I₄ through the 1.94Ω resistor.

As shown, R1 = 4.05Ω, R2 = 8.11Ω, R3 = 6.17Ω, R4 = 1.94Ω, I1 = 2.97A and E1 = 12V

Homework Equations

V=IR
ƩI in a junction = ƩI out of a junction
ƩV in a loop = 0

The Attempt at a Solution

I₁R₁+I₁R₂ -E₁ + I₂R₃ =0
I₁ = I₂ + I₄
So
I₄ =I₁ - ((-(I₁*R₁) - I₁R₂ + E₁)/R₃)

I don't have many tries left, so I want to know if my analytical solution is correct, and if I've just been making my error plugging the numbers back in.

 

[tiny-tim]

Hi BornSurvivor!

I₁R₁+I₁R₂ -E₁ + I₂R₃ =0
I₁ = I₂ + I₄

looks ok so far

but won't you need an equation involving E₂ ? ​

 

[BornSurvivor]

Nope! Those two equations were all I needed. It turns out I had mixed up the numbers for R2 and R3. :)