1. Copyright © 2009 Pearson Education, Inc. Admin: Mid-term date Friday March 20 th. Assignments : Second graded assignment is posted Make time for it – it’s a bit tougher than the first one Due Monday Use the hints. One or two of the questions are “tutorial” style, which are designed to add to the material I’ve covered in class. Use the textbook to help with these.

2. Copyright © 2009 Pearson Education, Inc. Today Using Kirchoff’’s laws

3. Copyright © 2009 Pearson Education, Inc. Junction rule (Kirchhoff’s current law): The sum of currents entering a junction equals the sum of the currents leaving it. Kirchhoff’s Rules I 3 =I 1 +I 2

4. Copyright © 2009 Pearson Education, Inc. Junction rule (Kirchhoff’s current law): This is a result of “conservation of charge” The charge has to go somewhere! Kirchhoff’s Rules

5. Copyright © 2009 Pearson Education, Inc. Loop rule (Kirchhoff’s Voltage Law): The sum of the changes in potential around a closed loop is zero. 0 = 12 - 400I - 290I Kirchhoff’s Rules

6. Copyright © 2009 Pearson Education, Inc. Why does the loop rule work? This is the result of “conservation of energy” All points of a circuit react instantaneously (at the speed of light) A “source” provides energy But Voltage is energy/charge (Joules/Coulomb) So, a 12V source provides 12 Joules of energy for each Coulomb of charge The energy is used up by transporting charge through resistance If the voltage of the source changes, the rate of charge transport changes If the resistance changes, the rate of charge transport changes V=IR ! http://regentsprep.org/Regents/physics/phys03/apotdif/ Kirchhoff’s Rules

7. Copyright © 2009 Pearson Education, Inc. Problem Solving: Kirchhoff’s Rules 1. Label each current, including its direction. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4.Solve the equations, being careful with signs. If the solution for a current is negative, that current is in the opposite direction from the one you have chosen. Kirchhoff’s Rules

8. Copyright © 2009 Pearson Education, Inc. Kirchhoff’s Rules Example: Using Kirchhoff’s rules. (see p685-6) Calculate the currents I 1, I 2, and I 3 in the three branches of the circuit in the figure. 1.Label currents 2.3 unknowns 3a. 1 Junction Rule 3b. 2 Loop Rules 4. Solve

9. Copyright © 2009 Pearson Education, Inc. Notes on Kirchhoff analysis The unknowns may not always be currents - they could be voltages or resistances – but the procedure is exactly the same If solutions to currents or voltages are negative, this means the real direction is opposite to what you originally defined To deal with current sources: the current is known, but assign an unknown voltage across it which has to be solved