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Introduction to Electrical & Computer Engineering Capacitors

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1 Introduction to Electrical & Computer Engineering Capacitors
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?

3 Passive element that stores energy in electric field
Capacitors Passive element that stores energy in electric field Parallel plate capacitor -12 Ɛo = x F/m Ɛr = 1 for air = 80 for water Circuits, FTUlaby, MMMaharbiz,CMFurse, © NTS Press 2015, Used with Permission by the Publisher

4 Capacitors: Where is the current?
Current = flow of charges I = dq/dt Air (no charges) Circuits, FTUlaby, MMMaharbiz,CMFurse, © NTS Press 2015, Used with Permission by the Publisher

5 Capacitors: Where is the current?
Current = flow of charges I = dq/dt Charges flow from voltage source towards capacitor + + + Air (no charges) Circuits, FTUlaby, MMMaharbiz,CMFurse, © NTS Press 2015, Used with Permission by the Publisher

6 Capacitors: Where is the current?
Current = flow of charges I = dq/dt + Charges accumulate on the top plate Note: This creates a voltage + + + a b + + + + + + + + + Air (no charges) The charges can’t cross the air space, because it is an open circuit, R = ∞ Circuits, FTUlaby, MMMaharbiz,CMFurse, © NTS Press 2015, Used with Permission by the Publisher

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

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

10 How to ‘Build with this’
C = ɛ A / d Two pieces of metal with foam between. Squish them (d) Slide them (A) Wet the foam (ɛ)

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

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

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

14 Capacitors: What happens when you first turn on the voltage?
Current immediately starts to flow. It is largest at the start. Charges flow from voltage source towards capacitor + + + Air (no charges) 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?
Current immediately starts to flow. But then the plates start to get ‘full’, so it decreases with time, and eventually goes to 0. + Charges accumulate on the top plate + + + + + + + + - - - - - Air (no charges) + + + + + The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate

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

17 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?

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

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

20 Capacitors: What happens when you first turn on the voltage?
Current immediately starts to flow. But then the plates start to get ‘full’, so it decreases with time, and eventually goes to 0. + Charges accumulate on the top plate + + + + + + + + - - - - - Air (no charges) + + + + + The + charges on top push away the + charges on the bottom. They flow towards the source and leave behind – charges on the bottom plate

21 What does a capacitor do to the current ?

22 What does a capacitor do to the current ?

23 What does a capacitor do to the current ?

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

25 Capacitors: What happens when you first turn on the voltage?
Meanwhile it starts to build a voltage. The voltage starts out as 0 and then grows to Vs. It can’t change instantly. Charges flow from voltage source towards capacitor + + a b + + Air (no charges) Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher

26 What does a capacitor do to the voltage ?

27 Vs

28 Vs 66% at t=RC t

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

30 RC Charging and Discharging

31 How can we use capacitors?
Energy Storage / Release

32 How can we use capacitors?
Stabilize power (reduce ripple)

33 Low Pass filter Noise Filter

34 Integrator

35 High Pass Filter DC Block

36 Differentiator

37 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?

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

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