1. Capacitance

2. Device that stores electric charge. Construction: A capacitor is two conducting plates separated by a finite distance Typically separated by an insulator or dielectric. Capacitor plates carry charges of the same magnitude but opposite charges. Capacitor Copyright ©2007 Pearson Prentice Hall, Inc.

3. Capacitance (C) Proportionality constant that relates the charge (q) on a capacitor plate to the potential difference (V) between the plates of a capacitor. Units: Coulomb/Volt = farad (F) Typical values are in micro-farads (μF) Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copywrited by Holt, Rinehart, & Winston

4. Dielectric A dielectric is an insulator; when placed between the plates of a capacitor it gives a lower potential difference with the same charge, due to the polarization of the material. This increases the capacitance. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copywrited by Holt, Rinehart, & Winston

5. Dielectric Constant (κ) The dielectric constant is a property of the material. E 0 electric field without the dielectric E electric field with the dielectric

6. Dielectric Breakdown occurs when the electric field becomes too large tearing electrons off the atoms allowing the material to conduct. Dielectric strength – electric field at which dielectric breakdown occurs.

7. Parallel Plate Capacitor Relationship: Capacitance depends on Area of the plate (A) – as the area the capacitance Separation between plates (d) – as separation the capacitance Dielectric constant of the material (  ) – as dielectric constant the capacitance Copyright ©2007 Pearson Prentice Hall, Inc.

8. Energy Storage Main function of a capacitor Electrical energy stored is found by Electrical energy density (u E ) Application: RAM storage In a RAM chip a capacitor is connected to a transistor switch with two inputs - an address line and a data line. A pulse on the address line turns on the transistor switch. With the switch on, a pulse on the data line will charge the capacitor. Charged capactior = 1, Uncharged capacitor = 0 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

9. Energy Storage Derivation for a Parallel Plate Capacitor Graphing Voltage vs Charge Area under the graph is energy stored

10. Capacitors in Circuits Parallel Circuits Voltage is the same across each capacitor. For 2 capacitors in parallel: q 1 =C 1 V and q 2 =C 2 V q total =q 1 +q 2 =(C 1 +C 2 )V Since C total = q total /V, C total = C 1 +C 2 … Capacitance adds up Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

11. Capacitors in Circuits Parallel Circuits Voltage is the same across each capacitor. Capacitance adds up Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copyright ©2007 Pearson Prentice Hall, Inc.

12. Capacitors in Circuits Series Circuits Each capacitor carries the same charge. q=q 1 =q 2 The total voltage is the sum of the voltages across each capacitor V total =V 1 +V 2 where V total = q/C total Then V total = q/C total = q/C 1 +q/C 2 Dividing by q, 1/C total = 1/C 1 +1/C 2 Total capacitance is found by summing the inverse of each individual capacitance. Copyright ©2007 Pearson Prentice Hall, Inc.

13. Capacitors in Circuits Series Circuits Total capacitance is found by summing the inverse of each individual capacitance. Capacitance addition is the inverse of resistance. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copyright ©2007 Pearson Prentice Hall, Inc.

14. Capacitors in Circuits Which of the following combinations of capacitors has the highest capacitance?

15. Capacitors in Circuits Which of the following combinations of capacitors has the lowest capacitance?

16. Charging a Capacitor When the switch is thrown, a current will flow for a short time and stop. The current will flow out of the positive battery terminal with electrons flowing in the opposite direction. Negative charge will accumulate on the left plate, while the same amount of positive charge will accumulate on the right plate. Charge will accumulate until the capacitor reaches its capacitance. Copywrited by Holt, Rinehart, & Winston

17. Charging a Capacitor Charging process The charging current I drops initial maximum I 0 down to zero. The stored charge on the capacitor increases zero to a final maximum value q 0. The potential difference (pd) across the capacitor V increases zero to a maximum value of ε The pd across the resistor drops initial maximum ε down to zero.

18. Charging a capacitor http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/capchg.gif

19. Charging a capacitor Charging Derivation

20. Discharging a Capacitor Discharging process The discharging current I drops initial maximum I 0 down to zero. The stored charge on the capacitor q drops initial maximum value q 0 down to zero The potential difference (pd) across the capacitor V decreases maximum value of V 0 down to zero The pd across the resistor is the same as the capacitor

21. Discharging a capacitor http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/capdis.gif

22. Discharging a capacitor Discharging Derivation

23. Slide 23-29 Exponential Decay Example A 10μF capacitor is discharged through a 20kΩ resistor. Calculate: (a)The time constant for the circuit and (b)the fraction of charge remaining after one time constant

24. The following circuits contain capacitors that are charged to 5.0 V. All of the switches are closed at the same time. After 1 second has passed, which capacitor is charged to the highest voltage? Slide 23-30 RC Circuits – Understanding check

25. The following circuits contain capacitors that are charged to 5.0 V. All of the switches are closed at the same time. After 1 second has passed, which capacitor is charged to the lowest voltage? Slide 23-30 RC Circuits – Understanding check