Examples Using Formal Circuit Methods 2.6 2000/07/10 2004/08/09 13:27:40.222 GMT-5 Don Johnson dhj@rice.edu Don Johnson dhj@rice.edu Roy Ha rha@rice.edu circuit formal circuit method node method Two examples of using the node method to solve for a circuit.

Node

The presence of a current source does not affect the node method greatly; just include it in writing KCL equations as a current leaving the node. The circuit has three nodes, requiring us to define two node voltages. The node equations are e 1 R 1 e 1 e 2 R 2 i in 0      (Node 1) e 2 e 1 R 2 e 2 R 3 0     (Node 2) Note that the node voltage corresponding to the node that we are writing KCL for enters with a positive sign, the others with a negative sign, and that the units of each term is given in amperes. Rewrite these equations in the standard set-of-linear-equations form. e 1 1 R 1 1 R 2 e 2 1 R 2 i in e 1 1 R 2 e 2 1 R 2 1 R 3 0 Solving these equations gives e 1 R 2 R 3 R 3 e 2 e 2 R 1 R 3 R 1 R 2 R 3 i in To find the indicated current, we simply use i e 2 R 3 .

Nodes Example

In this circuit, we cannot use the series/parallel combination rules: The vertical resistor at node 1 keeps the two 1 Ω resistors from being in series, and the 2 Ω resistor prevents the two 1 Ω resistors at node 2 from being in series. We really do need the node method to solve this circuit! Despite having six elements, we need only define two node voltages. The node equations are e 1 v in 1 e 1 1 e 1 e 2 1 0     (Node 1) e 2 v in 2 e 1 1 e 2 e 1 1 0     (Node 2) Solving these equations yields e 1 2 5 v in and e 2 5 13 v in . The output current equals e 2 1 5 13 v in . One unfortunate consequence of using the element's numeric values from the outset is that it becomes impossible to check units while setting up and solving equations.