1. Kirchhoff's Rules

2. Analyzing complex circuits by finding equivalent resistance works well when resistors are in series or parallel

3. Circuits
But, there are many circuits where no two resistors are in series or in parallel.
For these we need another set of tools… Kirchhoff's rules

4. Kirchhoff’s Rules
Junction Rule – the total current into a junction must equal the total current out of the junction.
Loop Rule – for a closed circuit loop, the sum of all the potential drops and potential gains around the closed loop is zero.

5. Junction Rule

6. Loop Rule
Step 1: Draw the current in each branch of the circuit. The direction is arbitrary.
Step 2: Mark each resistor with a + sign (where the current goes in) and – sign (where the current goes out). The signs need to be consistent with your choice of current direction.
Step 3: Apply the loop rule and junction rule to get as many independent equations as there are unknowns.
Step 4: Solve the system of equations.

7. Your Turn… write a loop equation for this circuit.

8. How many equations do we need?

9. Circuits

10. Homework
P. 637 #62-67, 79, 80, 81