Kirchoff’s Laws

Guide to solving complex circuits.

Step 1: Understanding the Laws

in outI I Junction Rule: “The sum of the currents into a junction equals the sum of the currents out of the junction”

1 2 3I I I

I1 I3

I2

Step 1: Understanding the Laws

1 2 3...totalV V V V Loop Rule: The sum of the potential differences across all of the elements around any closed loop must be zero.

40 V 0 V

Vtotal = 40 V

10 V 10 V 10 V 10 V + + +

40 V !!

Step 2: Applying the Laws

1. Choose the “loop” directions.

How are “Loop” Directions Determined?

1. Look at one “loop” at a time, disregard the rest…

2. Look for the largest voltage source.

3. Is it larger than the sum of any that oppose it?

Which is bigger?

4. The direction that current (I) would flow from that source is the “loop” direction.

Step 2: Applying the Laws

2. Write out the equation.

Start at the battery.

Apply Kirchoff’s 2nd Law:

3 26 V (33 ) (66 ) 0I I

Step 2: Applying the Laws

2. Write out the equation.

Then the voltage drops.

Apply Kirchoff’s 2nd Law:

3 26 V (33 ) (66 ) 0I I I3

Step 2: Applying the Laws

2. Write out the equation.

Then the voltage drops.

Apply Kirchoff’s 2nd Law:

3 26 V (33 ) (66 ) 0I I

Step 2: Applying the Laws

2. Write out the equation.

Add to be zero!

Apply Kirchoff’s 2nd Law:

3 26 V (33 ) (66 ) 0I I Loop Rule: The sum of the potential differences across all of the elements around any closed loop must be zero.

Step 3: MathLet’s try one…