# Circuit Theory/Superposition

## Goal

Split multisource circuit into smaller, simpler circuits, compute
current or voltage and add.

## Procedure

Pick one source, turn off all or set to zero all others:

-   Set Voltage Sources to V=0, doesn\'t care about current so is a
    short
-   Set Current Sources to I=0, doesn\'t care about the voltage so turns
    into an open

## Example 1

Find the current through the 3 ohm resistor assuming moving left to
right is positive:

<File:Example16a.png%7CThe> original circuit is equal to
<File:Example16b.png%7Cthis> circuit where i = 24/5 plus
<File:Example16c.png%7Cthis> circuit where i = -14/5 (current divider)
plus <File:Example16d.png%7Cthis> circuit where i = -3/5.

The total current in the direction shown on the original diagram is
going to be:
$\frac{24}{5} - \frac{14}{5} - \frac{3}{5} = \frac{7}{5} amp$

## Example 2

Find the current through the 4 ohm resistor assuming moving left to
right is positive:

<File:Example17a.png%7CThe> original circuit is equal to
<File:Example17b.png%7Cthis> circuit which can be re-drawn as
<File:Example17bs.png%7Cthis> circuit where i = 35/3 = 11.67 plus
<File:Example17c.png%7Cthis> circuit which can be re-drawn as
<File:Example17cs.png%7Cthis> circuit where i = -11/36 = -.3056 plus
<File:Example17d.png%7Cthis> circuit which can be re-drawn as
<File:Example17ds.png%7Cthis> circuit where i = 25/18 = 1.3889 (current
divider)

$i = 35/3 - 11/36 + 25/18 = 51/4 = 12.75 amps$

Simulation at circuit
lab confirms the
answer:

!DC Simulation at Circuit
Lab

