1. Today 3/28  Circuits  Current  Potential (same as always)  Capacitance (energy and in circuits)  HW:3/28 “Circuits 3” Due Wednesday 4/2  Note: Watch out for “round off” errors, keep three decimal places to the end on all circuit homeworks.

2. Voltage Model  Voltage: how much energy each coulomb of charge gains (battery) or loses (bulb) in going through an element. (as usual)  More glow, more voltage.  The Loop Rule:  What goes up, must come down!  V A,A = 0, voltage rises and drops must must cancel around any loop.

3. Current Model Fails A B Compare B to D B gets all of the current through A. D gets half of the current through C. But the current through C is bigger than the current through A. C ED Can’t be sure which is brighter!!! less current more current all 1/21/2 1/21/2

4. Voltage Model A B Compare B to D C ED C brighter than D C has more voltage than D VCVC VDVD Compare the voltages across B and D. More volts more glow! Recall current for B and D. VAVA VBVB think loops V V

5. Voltage Model The voltage for series elements SPLITS because it adds up to the battery voltage. The voltage splits equally for identical Rs. Otherwise, the voltage drop is greater across the greater R. A B in series

6. Find Equivalent Resistance 12 V ?? R eq = 6  22 66 88 88 99 77 55 12 V 44 66 33 12 

7. Find current through the battery 22 66 88 88 99 77 55 12 V 66 I = 2 Amps 12 V It is the same as the current through R eq. R eq = 6 

8. Current through each element 22 66 88 88 99 77 55 12 V 66 I = 2 Amps What is the current through each resistor? 12 V 1 Amp 0.5 Amp 0.25 Amp each What is the voltage across each resistor? 2 Amps

9. Voltage across each element 22 66 88 88 99 77 55 12 V 66 I = 2 Amps What is the current through each resistor? 12 V 5 V 9 V 3 V 1 V 2 V each What is the voltage across each resistor? 7 V

10. Kirchhoff’s Rules, Loop  The sum of all voltages around any closed loop is zero. (what goes up must come down)  or  V A,A = 0  !!must keep track of ups and downs!! (+/-)

11. Kirchhoff’s Rules, Junction  The sum of all currents at any junction is zero. (what goes in must come out)  !!must keep track of ins and outs!! (+/-)

12. Capacitors Capacitance tells me how many coulombs of charge are stored in a capacitor when it has 1 Volt across it. A 25  F capacitor will have 25  C of charge on it when it has 1 volt across it. Think of capacitance as “coulombs per volt”. Units:coulombs per volt or “Farads” Equation: C = q/V

13. Capacitors Think of storing propane in a tank. The amount of propane depends on the pressure just as the amount of charge depends on voltage. We will use parallel plate capacitors so that all ideas from parallel plates apply. V = EdE =  /  o (two plates)  = Q/A

14. Capacitors How much charge is on the capacitor? Think “6x10 -6 Coulombs per Volt and you won’t need the equation! 12 V 6F6F6F6F 72x10 -6 C or 72  C

15. Capacitors What is the E-field inside the capacitor if the plates have an area of 1 m 2 ? 12 V 6F6F6F6F Q = 72x10 -6 C or 72  C E =  /  o = 8.2x10 6 N/C What is the distance between the plates? V = Ed d = 12/8.2x10 6 = 1.5x10 -6 m Note that capacitance depends on the area and separation distance

16. Capacitors and Energy How many Joules of energy are stored in the capacitor? 12 V 6F6F Ask yourself, “How much work must be done to charge the plates?”

17. Capacitors and Energy How many Joules of energy are stored in the capacitor? 12 V 6F6F As the battery moves charge from one plate to another, the potential difference increases from zero to 12 V. The average is 6 V and the energy stored is q times 6 V (q  V ave ). Energy = q  V ave = 1 / 2 q  V = 1 / 2 C  V 2 C = q/  V

18. Capacitors with Resistors Will current flow when the switch is closed? 12 V 6F6F 66 6F6F Yes, but only for an instant until the capacitor is charged. Yes, but it will take longer to charge the capacitor.

19. Capacitors with Resistors Describe current and voltage long after the switch has been closed. 12 V 6F6F 66 6F6F No current, 12 V across the capacitor. No current, 12 V across the capacitor, zero V across the resistor. Loop rule still applies! V = IR for resistors still applies!

20. Capacitors with Resistors Describe current and voltage long after the switch has been closed. 12 V 6F6F 22 2 Amps through the battery and both resistors. 4 V across 2  and 8 V across the capacitor and 4  Loop rule still applies! V = IR for resistors still applies! 44

21. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

22. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

23. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

24. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

25. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

26. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

27. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other.

28. Charging Capacitors in Series The same amount of charge that enters one side of a capacitor, leaves the other. Capacitors in series will always have the same charge on them. (what goes around, comes around) This is true even if they are not of equal capacitance! Current will flow until the sum of the voltages across the capacitors equals the battery voltage. (loop rule)

29. Capacitors in Series Find the charge on each capacitor and the voltage across each capacitor. The battery is 30V. 25  F 50  F They are in series so the charge on each is the same. Capacitance means “coulombs per volt” so the one with twice the capacitance has half the volts. 1 2 V 1 = 20V, V 2 = 10V, Q 1 = 500  C, Q 2 = 500  C

30. Capacitors in Parallel Find the charge on each capacitor and the voltage across each capacitor. The battery is 30V. They are in parallel so the voltage across each is the same, each equal to 30V. Q 1 = 750  C, Q 2 = 1500  C 25  F50  F 12

31. Series and Parallel  Objects in series have the same current through them. This is why capacitors in series always have the same charge on them.  Objects in parallel have the same voltage across them.

32. Ohm’s law, loops & junctions  V = IR true for entire circuits as well as individual elements.  Voltage changes summed around any closed loop equal zero.  Current divides and combines at junctions like water in pipes. What enters the junction must also leave.

33. Homework R 1 =20  100  R 1 =20  30  F 15V