Find currents and voltages - 2 batteries & 3 resistors

[kamhogo]

Homework Statement

Find I1, I2, I3 as well as the voltages across each resistor.

R1= 50 ohms
R2= 220 ohms
R3= 150 ohms

Homework Equations

Kirchhoff's loop law
Kirchhoff's junction law

The Attempt at a Solution

Loop 1: Starting from the negative terminal of the 10V battery (ccw)

10V - 50 (I1) - 220 (I2) = 0

Loop 2: Starting from junction a (ccw). Note I added an I4 through R3 to try and make things easier for me to visualize .

- 150 (I4) + 5 V + 0 (I3) + 220 (I2) = 0

Junction law
I1 = I2 + I4Loop 1
10V - 50 I2 - 50 I4 - 220 I2 =0
10V - 270 I2 - 50 I4 = 0

Loop 2
I2= (150 I4 - 5 V )/220 = 0.682 I4 - 0.0227 A

Loop 1
10V - 270 (0.682 I4 - 0.0227 A) - 50 I4 = 0
- 234.14 I4 = -16. 129
I4 = 0.069 A
I2= 0.024 A
I1= 0.093 A
I3 = ??

Voltages across :
R1 ==> 4.65 V
R2 ==> 5.28 V
R3 ==> 10.35 VI can't find I3. Is it possible that R2 "receives" a portion of I3 downstream (...I5. ...) in addition to having I2 go through R2 it upstream? ? Or maybe I3 is infinitely big (ideal wire model, goes from the positive terminal of the 5V battery and then directly to the negative terminal of the 10V battery)?

 

[gneill]

I don't know why you've introduced I4. The branch has two components in series, so they MUST carry the same current, and that's already labelled I3.

 

[kamhogo]

I don't know why you've introduced I4. The branch has two components in series, so they MUST carry the same current, and that's already labelled I3.Oooh. I see it now. Thanks!

View attachment 99436

 

[kamhogo]

Resolved.