1. Introduction to Electrical & Computer Engineering Capacitors 1 Dr. Cynthia Furse University of Utah Dr. Cynthia Furse University of Utah

2. Capacitors What is Capacitance ? How does it relate to current & charges? Explain the effect of ɛ, A, d What does it do to a voltage and current? 2

3. Capacitors Passive element that stores energy in electric field Parallel plate capacitor Ɛ o = 8.854 x 10 F/m Ɛ r = 1 for air = 80 for water -12 Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

4. Capacitors: Where is the current? Current = flow of charges I = dq/dt Air (no charges ) Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

5. Capacitors: Where is the current? Current = flow of charges I = dq/dt Air (no charges) + + + Charges flow from voltage source towards capacitor Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

6. Capacitors: Where is the current? Current = flow of charges I = dq/dt Air (no charges) + + + + + + + + + + + + Charges accumulate on the top plate + a b + + + + Note: This creates a voltage Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher The charges can’t cross the air space, because it is an open circuit, R = ∞

7. Capacitors: Where is the current? Current = flow of charges I = dq/dt Air (no charges) + + + + + + + + + Charges accumulate on the top plate + a b + + + + Note: This creates a voltage The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate +++ - - - - - + +

8. Conduction = Displacement Current Conduction Current = flow of charges I = dq/dt Air (no charges) + + + + + + + + + Charges accumulate on the top plate + a b + + + + Note: This creates a voltage The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate +++ - - - - - + + Displacement Current = appearance of the flow of charges, induced by time varying electric field Conduction Current = flow of charges I = dq/dt

9. Capacitors: Where does this mean? C = ɛ A / d Air (no charges) + + + + + + + + +++ - - - - - + + Greater A can store more charges Larger d reduces attraction between the charges on the two plates Larger ɛ increases attraction between the charges

10. How to ‘Build with this’ 10 C = ɛ A / d Two pieces of metal with foam between. Squish them (d) Slide them (A) Wet the foam ( ɛ ) http://www.chenyang-ism.com/CapaSensorPosi.htm

11. Capacitors What is Capacitance ? How does it relate to current & charges? Explain the effect of ɛ, A, d 11

12. Electrical Properties of Capacitors Capacitance – current, charge, voltage, power, energy What happens at DC? Series and Parallel 12

13. Capacitors: Current & Charge Air (no charges ) Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher Current = flow of charges I = dq/dt At DC there is no change with time (d/dt = 0) So…I=0 >>>> OPEN CIRCUIT

14. Capacitors: What happens when you first turn on the voltage? Current immediately starts to flow. It is largest at the start. Air (no charges) + + + Charges flow from voltage source towards capacitor Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

15. Capacitors: What happens when you first turn on the voltage? Air (no charges) + + + + + + + + + Charges accumulate on the top plate The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate +++ - - - - - + + Current immediately starts to flow. But then the plates start to get ‘full’, so it decreases with time.

16. Capacitors: What happens when you first turn on the voltage? Air (no charges) + + + Charges flow from voltage source towards capacitor Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher a b + + Meanwhile it starts to build a voltage. The voltage starts out as vs and then grows. It can’t change instantly.

17. Capacitors: What happens when you first turn on the voltage? Air (no charges) + + + + + + + + + Charges accumulate on the top plate + a b + + + + Note: This creates a voltage The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate +++ - - - - - + + Meanwhile, this starts to create

18. What does a capacitor do to the current ? 18

19. What does a capacitor do to the current ? 19

20. What does a capacitor do to the current ? 20

21. What does a capacitor do to the current ? 21 Vs/R 36% at t=RC

22. What does a capacitor do to the voltage ? 22

23. 23 Vs 66% at t=RC

24. What does a capacitor do to a voltage and current? t=0: SHORT CIRCUIT t=∞: OPEN CIRCUIT 24 Current changes Instantly Voltage changes slowly At ‘steady state’ Current =0 At ‘steady state’ Voltage is Vs

25. Charging and Discharging 25 http://lwn.net/Articles/250967/

26. How can we use capacitors? Energy Storage / Release 26

27. How can we use capacitors? Stabilize power (reduce ripple) 27 http://www.beavisaudio.com/techpages/Caps/

28. Low Pass filter Noise Filter 28

29. Integrator 29 http://www.piclist.com/images/www/hobby_elec/e_ckt1.htm

30. High Pass Filter DC Block 30

31. Differentiator 31 http://www.piclist.com/images/www/hobby_elec/e_ckt1.htm

32. Introduction to Electrical & Computer Engineering Antelope Island, Great Salt Lake, Utah 32 Dr. Cynthia Furse University of Utah