Ex:           In the circuit below, use Kirchhoff's voltage and current laws to write equations relating voltages and currents.

 

 

 

Answer: -i1 + i2 - ig = 0

                  vg - v1 - v2 = 0

 

Sol'n:      We sum the currents flowing out of the top center node. Writing an equation for the bottom node would be redundant. Recall that we always have one extra node.

                  Because writing a v-loop equation for the right inner loop would require defining a voltage for a current source, we write a v-loop equation for only the left loop. Note that the only larger loop containing the right inner loop would also require defining a voltage for the current source. Thus, a voltage loop equation for the right side is unnecessary.

                  Our voltage loop on the left starts from the lower left and proceeds in a clockwise direction. We may start voltage loops wherever we desire, but being consistent tends to improve accuracy.