1. Copyright © 2009 Pearson Education, Inc. Admin: Lab today: Light bulb and resistors II: current - voltage (I - V) curves Don’t forget to complete the pre-lab. Proposed mid-term date: Wednesday March 18 th. Assignments : Still a few people not registered for Mastering Physics Second graded assignment is posted. Due Monday March 2 nd Grading setting changed from 3 to 4 attempts. If you’re not completely sure of your answer, use the hints. Don’t forget the other resources available to you – my office hours, my email, the discussion TAs and their office hours and emails.

2. Copyright © 2009 Pearson Education, Inc. Today Sources Finishing up combination rules Kirchoff’’s laws

3. Copyright © 2009 Pearson Education, Inc. More on Sources Sources and Loads –Source + load = simplest description of any electrical system –Voltage sources and current sources –provide prescribed voltages / currents –Ideal sources: can provide any amount of energy –In the ideal case, Voltage / Current values are not affected by load –Ideal voltage source: Output voltage does not change with current Current supplied is determined by load Zero internal resistance –Ideal current source: Output current does not change with voltage Voltage generated is determined by load Infinite internal resistance battery

4. Copyright © 2009 Pearson Education, Inc. Practical Voltage Sources Modelled with an ideal source and a series resistor Ideal voltage source: r S =0 So for a practical voltage source, the output voltage depends upon R L If r S << R L, v L = v S, independent of R L voltage divider rule

5. Copyright © 2009 Pearson Education, Inc. Some voltage sources

6. Copyright © 2009 Pearson Education, Inc. EMFs in series in the same direction: total voltage is the sum of the separate voltages. Series and Parallel EMFs

7. Copyright © 2009 Pearson Education, Inc. EMFs in series, opposite direction: total voltage is the difference (but the lower- voltage battery is charged). Series and Parallel EMFs; Battery Charging

8. Copyright © 2009 Pearson Education, Inc. EMFs directly in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf. Series and Parallel EMFs

9. Copyright © 2009 Pearson Education, Inc. Some current sources

10. Copyright © 2009 Pearson Education, Inc. Practical Current Sources Modelled with an ideal source and a parallel resistor Ideal current source: r S =  The output current now depends upon R L If r S >> R L, i L = i S, independent of R L current divider rule

11. Copyright © 2009 Pearson Education, Inc. Current sources in parallel provide a current equal to their sum. Current sources in series does not happen. Series and Parallel EMFs

12. Copyright © 2009 Pearson Education, Inc. Circuit analysis method 1: Apply element combination rules Series resistors Parallel resistors Series voltage sources Parallel current sources

13. Copyright © 2009 Pearson Education, Inc. Another Example R1=10Ω R2=20Ω R3=30Ω V=10V Find the equivalent resistance and the current at I R=22Ω I= 10V/22Ω = 0.45V