2. Physics 223

3. 28. Direct Current (DC) Circuits 28.1 EMF and Voltage 28.2 Resistors in Series and Parallel 28.3 Kirchhoff’s Rules 28.4 RC Circuit 28.5 Ammeters and Voltmeters 28.6 Household Wiring

4. Electric Battery + - The battery converts chemical energy to electrical energy. It is a source of potential difference or voltage. This is used to drive electrons “downhill” through a conductor (resistor)

5. Electric Current and Ohm’s Law I = Q / t current = charge / time V = I R voltage = current x resistance

6. 28.1 EMF and Voltage V = ɛ - I r r is the “hidden” internal resistance of the battery.

7. 28.2 Bulbs in Series and Parallel A.L1 and L2 are in series B.L1 and L2 are in parallel C.L3 and L4 are in series D.None of the above L3 L4 L1L2

8. Bulbs in Series and Parallel L1 and L2 are in series and L3 and L4 are in parallel L3 L4 L1L2

9. Bulbs in Series and Parallel A.I 1 = I 2 B.V 1 = V 2 C. I 3 = I 4 D. None of the above L3 L4 L1L2

10. Bulbs in Series and Parallel Series Parallel I 1 = I 2 V 3 = V 4 L3 L4 L1L2

11. Example 28.1... Series Circuit Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors R1 = 3ΩR2 = 6Ω V = 12V

12. Solution 28.1... Series Circuit R eq = R 1 + R 2 R1 = 3ΩR2 = 6Ω V = 12V R eq = 9Ω V = 12V I = 12/9 =4/3 A V1 = 4/3 x 3 = 4 V V2 = 4/3 x 6 = 8 V

13. Example 28.2... Parallel Circuit 12V R1 =6 Ω R2 = 3 Ω Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors

14. Solution 28.2... Parallel Circuit 12V R1 =6 Ω R2 = 3 Ω 1/ R eq = 1/R 1 + 1/R 2 R eq =2Ω V = 12V I 1 = 12/6 =2 A I 2 = 12/3 =4 A

15. Example 28.3... Series /Parallel Combo Special! R1 =3Ω R2 =6Ω R3 =4Ω V =12V Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors

16. Solution 28.3... Series /Parallel Combo Special! R1 =3Ω R2 =6Ω R3 =4Ω V =12V Req =2Ω R3 =4Ω V =12V I eq = 12/6 =2A V eq = 2 x2 = 4V V 1 = V 2 = 4V I 1 = 4/3 A and I 2 = 2/3 A

17. 28.3 Kirchhoff’s Rules  I = 0 (Junction)  V = 0 (Loop)

18. RC Charging Circuit V C = V 0 (1 - e -t /RC ) V R = V 0 e -t /RC V0V0 VRVR t VCVC

19. RC Discharging Circuit V C = V 0 e -t /RC V R = V 0 e -t /RC VRVR t =VC=VC

20. 28.5 Ammeters and Voltmeters A V Ammeter measures current Ammeter is connected in series Ammeter has a LOW resistance Ammeter is tricky to hook up Voltmeter measures voltage Voltmeter is connected in parallel Voltmeter has a HIGH resistance Voltmeter is easy to hook up

21. That’s all folks!