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:

• 
  The original circuit is equal to
• 
  this circuit where i = 24/5 plus
• 
  this circuit where i = -14/5 (current divider) plus
• 
  this 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:

• 
  The original circuit is equal to
• 
  this circuit which can be re-drawn as
• 
  this circuit where i = 35/3 = 11.67 plus
• 
  this circuit which can be re-drawn as
• 
  this circuit where i = -11/36 = -.3056 plus
• 
  this circuit which can be re-drawn as
• 
  this circuit where i = 25/18 = 1.3889 (current divider)

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

Simulation at circuit lab confirms the answer: