Circuit question: Find size and direction of current at P

[Faris A]

Homework Statement

Homework Equations

I = I₁ + I₂ ... + I_n
R = R₁ + R₂ ... + R_n
1/R = 1/R₁ + 1/R₂ ... + 1/R_n

The Attempt at a Solution

Let I₁ = I₂ + I₃ where I₁ is the current on the top wire, I₂ the current on the middle wire and I₃ the current on the bottom wire.

4 = 10I₂ + 20I₁
//This is what I started trying but I can kind of tell that this is wrong

 

[cnh1995]

4 = 10I2 + 20I1
//This is what I started trying but I can kind of tell that this is wrong

If you assume I1 to be clockwise and I2 to be from right to left, this equation is correct. Assume a direction for I3 and write another equation. Your directions may be wrong, but that will just give you a negative value for the current.

 

[Faris A]

If you assume I1 to be clockwise and I2 to be from right to left, this equation is correct. Assume a direction for I3 and write another equation. Your directions may be wrong, but that will just give you a negative value for the current.

If 4 = 20I₁ + 10I₂ is correct then 12 = 10I₃ + 10I₂ is correct
I₁ = I₂ + I₃
4 = 20(I₂ + I₃) + 10I₂
4 = 20I₃ + 30I₂
12 = 10I₃ + 10I₂ can be made into 24 = 20I₃ + 20I₂
Using simultaneous equations: 20 = -10I₂
I₂ = -2

But is this correct?

 

[Faris A]

If 4 = 20I₁ + 10I₂ is correct then 12 = 10I₃ + 10I₂ is correct
I₁ = I₂ + I₃
4 = 20(I₂ + I₃) + 10I₂
4 = 20I₃ + 30I₂
12 = 10I₃ + 10I₂ can be made into 24 = 20I₃ + 20I₂
Using simultaneous equations: 20 = -10I₂
I₂ = -2

But is this correct?

dw I figured out where I was going wrong