The above circuit can be split up into three loops and two nodes. The three loops and their corresponding equations are:
Kirchoff's Rule
In electronics there are a pair of axioms that describe circuits with batteries and resistors. (A resistor can be any electrical appliance, a light bulb, a TV, a radio, etc.) These axioms are called Kirchoff's rules. The first rule represents conservation of energy. The amount of energy any charge gains in the process of traversing a circuit must be exactly balanced by the amount of energy the charge loses. The energy per charge is called potential (or voltage). The second rule represents conservation of charge. If a given amount of charge is flowing in a circuit over a time interval (we call this current) and the circuit forks, then some of the current will go into each branch of the fork. The sum of the currents exiting the fork will equal the sum of the currents entering the fork. In electronics the fork is referred to as a node or a junction. Algebraically each complete circuit or loop yields an equation and each node yields an equation.
The above circuit can be split up into three loops and two nodes. The three loops and their corresponding equations
are:
Loop 1:
9-3I3 + 4-2I2 = 0
Loop 2:
9 - 3I3- 6I6 = 0
Loop 3:
2I2 - 4 - 6I6 = 0
The two nodes and their equations are:
Node A:
I3 = I2 + I6
Node B:
I2 + I6 = I3
Since there are only three unknowns, only three of the five equations are needed. Notice that the two node equations are really the same, so only use one of the node equations. Pick any two of the loop equations to obtain the three equations necessary. Now solve this system of equations and find the currents in each of the three branches.