1. Internal Resistance Real batteries have a small internal resistance, r, which is small but non-zero Terminal voltage:  V  V b  V a P10 -    I r   I r (In reality, due to r, even if you short the leads you don’t get infinite current). In this course, when internal resistance or terminal voltage is not mentioned, we typically don’t need to consider the battery’s internal resistance

2. Kirchhoff’s Loop Rules are important for complicated circuits. Especially when there is more than 1 battery. P10 - 2

3. Kirchhoff’s Rules 1.Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction. I1 I2 I3I1 I2 I3 P10 - 3

4.  V    E  ds  0 Close path Kirchhoff’s Rules 2.Sum of potential differences across all elements around any closed circuit loop must be zero. � P10 - 4

5. Steps of Solving Circuit Problem P10 - 5 1.Straighten out circuit (make squares) 2.Simplify resistors in series/parallel 3.Assign current loops (arbitrary) 4.Write loopequations (1 per loop) 5.Solve

6. Example:Simple Circuit You can simplify resistors in series (but don’t need to) What is current through the bottom battery? P10 - 6

7. Example:Simple Circuit Start at a in both loops Walk in direction of current  2   I 1 R   I 1  I 2  R  0   I 2  I 1  R    0  2   I 1 R    0  I 1  R  Add these:  I 2  I 1  R    I 2  P10 - 7 I1I1 R  I2 0I2 0 We wanted I 2 :

8. P10 - 34 Group Problem:Circuit Find meters’ values.All resistors are R, batteries are  HARDEREASIER

9. Voltage Meter A ideal Voltage meter can be considered to have a infinite resistance. When we use it to measure the voltage between two point, it does not let current flow through it and doesn’t changed the voltage between those two points. The current through a Voltage meter is ZERO.

10. Ampere Meter A ideal Ampere meter can be considered to have zero resistance. When we use it to measure the current along any path, it doesn’t need any voltage drop though the Ampere meter, and doesn’t change the current in that path. The Voltage difference across an Ampere meter is ZERO.

11. P10 - 34 Group Problem:Circuit Find meters’ values.All resistors are R, batteries are  HARDEREASIER

12. PRS Questions: More Light Bulbs P10 - 41