1. Circuit Analysis Chapter 18 AP Physics: M. Blachly

2. Review What is the total resistance of this circuit? Find the current that flows out of the battery. What is the power dissipated in the 200 ohm resistor?

3. A new problem: What is the power dissipated in the 200 ohm resistor?

4. Kirchoff’s Laws The Basic Idea: What goes in must come out. If you walk a complete loop around the block, you must end up back where you started. Restated in terms of current and voltage The sum of the currents in any junction must be equal to zero The sum of the voltage drops around any closed loop must be zero.

5. Application to first Problem

6. Kirchoff’s Laws The sum of the currents in any junction must be equal to zero Pick a direction for the current in each branch and label it. Don’t worry if you are wrong: the solution will fix that The sum of the voltage drops around any closed loop must be zero. Going in the direction of your current, the voltage will drop through a resistor. If going opposite I, the voltage will increase. Going backwards through a battery will drop the voltage.

7. Kirchoff’s Results The application of Kirchoff’s Laws will yield n equations with n unknowns. We can solve these equations by Substitution Elimination Matrix operations.

8. Equations We can now use K’s laws to find the system of equations that describe our circuit:

9. Matrices and the Ti-8x Nice reference for entering matrices on your calculator: http://www.itc.csmd.edu/mth/ti83/matrix/enter.htm Followed by one for operations on matrices: http://www.itc.csmd.edu/mth/ti83/matrix/rref.htm

10. Matrix Representation

11. Matrix Operations Putting the matrix in Reduced Row Echelon form yields

12. Example 2: Your turn