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Circuit Analysis

Circuit Analysis. Chapter 18 AP Physics: M. Blachly. 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?. A new problem:. What is the power dissipated in the 200 ohm resistor?.

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Circuit Analysis

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  1. CircuitAnalysis 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

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