1. Guide to solving complex circuits.
Kirchoff’s Laws
Guide to solving complex circuits.

2. Step 1: Understanding the Laws
Junction Rule: “The sum of the currents into a junction equals the sum of the currents out of the junction” I1 I3 I2

3. Step 1: Understanding the Laws
Loop Rule: The sum of the potential differences across all of the elements around any closed loop must be zero.
Vtotal = 40 V
40 V
0 V
10 V +
10 V
10 V
10 V
40 V !!

4. Step 2: Applying the Laws
1. Choose the “loop” directions.

5. 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?
4. The direction that current (I) would flow from that source is the “loop” direction.
Which is bigger?

6. Step 2: Applying the Laws
2. Write out the equation.
Apply Kirchoff’s 2nd Law:
Start at the battery.

7. Step 2: Applying the Laws
2. Write out the equation.
Apply Kirchoff’s 2nd Law: I3
Then the voltage drops.

8. Step 2: Applying the Laws
2. Write out the equation.
Apply Kirchoff’s 2nd Law:
Then the voltage drops.

9. Step 2: Applying the Laws
2. Write out the equation.
Apply Kirchoff’s 2nd Law:
Loop Rule: The sum of the potential differences across all of the elements around any closed loop must be zero.
Add to be zero!

10. Step 3: Math
Let’s try one…