Question

Find the current (I1, I2, and I3) in each branch of the circuit using Kirchhoff's Laws.

Answer 1

Consider a simple circuit in figure above.

Use the voltage law for loops 1 and 2 correspondingly, then add an equation by the current law:

$$12=10I_1+20I_2,\\ -20I_2+30I_3=0,\\ I_1=I_2+I_3.$$

So, we have three equations and three unknown values, which means that we can solve this system with any method we know from the course of math. The roots are

$$I_1=0.55\text{ A},\\ I_2=0.33\text{ A},\\ I_3=0.22\text{ A}.$$