I'd like to help a fellow student in getting the ins and outs of Kirchhoff's current and voltage law. Thing is, it's been a while for me...
I remember that the current law dictates the sum into and out of a node to be zero, and the sum of the voltage inside a loop again zero. I may also assume the initial current directions.
The circuit in question has 10 resistors and five ideal voltage sources.
This yields I1 - I5 as the unknowns so I need a system of five linear equations:
- Loop 1: 0 = V1 - I1 * (R1 + R2 + R3) - I2 * R5 - V2
- Loop 2: 0 = V2 + I2 * R5 + V5 - I4 * R6 - V3 - I3 * R4
- Loop 3: 0 = V3 + I4 * R6 - I5 * (R7 + R8 + R9 + R10) + V4
- Node 1: 0 = I1 - I2 - I3
Node 2: 0 = I3 - I4 - I5
Plugging this into Mathemathica I get
- I1 = 2.1 mA
- I2 = 0.36 mA
- I3 = 1.74 mA
- I4 = -1.72 mA
- I5 = 3.45 mA
I am not so much interested in the actual values but if my understanding is correct.
Thanks for reading! Chris