1. Kirchhoff’s Rules Illustrated

2. Kirchoff’s Rules Determine the magnitude and direction of current through the various resistors. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3

3. Kirchoff’s Rules Assume a direction to traverse the loop. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3

4. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge!!! I 1

5. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge!!! I 2

6. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge!!! I 2

7. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge!!! I 2

8. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge!!! I 3

9. Kirchoff’s Rules Assume a direction of current flow. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Trace out the current. Remember conservation of charge: I1 = I2 + I3!!! I 1

10. Kirchoff’s Rules Pick a starting point for each loop. R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3

11. Kirchoff’s Rules Traverse the loop in the direction YOU have chosen. End where you start!! R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Keep track of all the Potential differences encountered and sum to zero. = 0 R 1 -I 1 ε 2 + R 3 + 3 + R 6 1 + R 4 ε 1 + 1

12. Kirchoff’s Rules Traverse the right loop in the direction YOU have chosen. End where you start!! R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 Keep track of all the Potential differences encountered and sum to zero. = 0 R 5 -I 2 ε 3 + R 2 + 2 - ε 2 + I R 3 3

13. Kirchoff’s Rules Summary: R 2 R 4 R 6 R 3 R 5 R 1 ε 1 ε 2 ε 3 = 0 R 1 -I 1 ε 2 + R 3 + 3 + R 6 1 + R 4 ε 1 + 1 = 0 R 5 -I 2 ε 3 + R 2 + 2 - ε 2 + I R 3 3 I 1 = I 3 I 2 +

14. As soon as switch is thrown into position a, there is a current flow throughout the entire circuit. After a very long time, current stops flowing through resistor R. This is equivalent to stating that the potential difference across R is zero after a long time after the switch is thrown to position a. (Charge stops “flowing” and is stored in the capacitor). C R ε a b Kirchhoff’s Rules (RC – circuit)

15. Applying Kirchoff’s rules: C R ε a b Kirchhoff’s Rules (RC – circuit)

16. Applying Kirchoff’s rules: leads to the expression: C R ε a b Kirchhoff’s Rules (RC – circuit)

17. Thus the total charge on the capacitor builds up over time, and the current through the circuit comes to a halt! (All potential difference is across the capacitor and none over the resistor.) The total charge is expressed as: C R ε a b Kirchhoff’s Rules (RC – circuit)

19. What about discharging the capacitor through the resistor R? Wait a really long time (t >> RC), and switch S to position b. C R ε a b Kirchhoff’s Rules (RC – circuit)

20. Applying Kirchoff’s rules: leads to the expression: Kirchhoff’s Rules (RC – circuit)

22. Verify RC – Circuit Discharge!