|
|
By: Neil E.
Cotter
|
CIRCUITS
|
|
|
Kirchhoff's laws
|
|
|
Current sums at nodes
|
|
|
|
|
|
|
Def: A circuit
node is any point to which three or more circuit elements are attached.
Note: The goal
of writing current summation and voltage loop equations is to obtain n
equations in n unknowns that we can solve to find all the currents and
voltages in a circuit.
Tool: Nodes
connected by wires are considered to be a single node.
Tool: We set the
sum of currents measured as flowing out of a node to zero. If the current
measurement arrow points toward a node, that current appears with a minus sign
in the current-sum equation.
Tool: We skip
current sums for nodes where we would be forced to define a current for a
voltage source. Writing an equation for such a node adds a new variable and a
new equation. Thus, we merely create more equations in more unknowns rather
than moving closer to the goal of writing n equations in n
unknowns.
Tool: There is
always at least one node we may skip when writing current-sum equations. The
equation for that node would be redundant.
Tool: When
necessary, we supplement current sum equations with equations that equate
currents flowing in circuit elements that are in series.
Note: Summing
the currents flowing into a node yields an equation that is equivalent to the
equation for summing the currents flowing out of that node. Multiplying one
equation by -1 on both sides yields the other equation.
Note: Summing
currents measured as flowing into a node and setting that sum equal to currents
measured as flowing out of that node yields an equation equivalent to setting
the sum of all currents measured as flowing out of the node to zero.