Introduction to Electrical Computer Engineering Capacitors Dr Cynthia

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

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

Capacitors Passive element that stores energy in electric field Parallel plate capacitor -12 Ɛo = 8. 854 x 10 Ɛr = 1 for air = 80 for water Circuits, Second Edition by Fawwaz T. Ulaby and Michel M. Maharbiz, © NTS Press, Used with Permission by the Publisher F/m

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

Capacitors: Where is the current? Charges flow from voltage source towards capacitor 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

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

Capacitors: Where is the current? Current = flow of charges I = dq/dt + Charges Note: This creates a voltage accumulate on the top plate + + + ++ - + ++ + + a + +++ + Air (no charges) b 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 = Displacement Current Conduction Current = flow of charges I = dq/dt Note: This + Charges creates a voltage accumulate on the top plate + + + + ++ a Displacement Current + + = appearance of the + flow of charges, - induced by time b varying electric field + + +Conduction Current = flow of charges 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 I = dq/dt

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

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) http: //www. chenyang-ism. com/Capa. Sensor. Posi. htm 10

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

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

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

Capacitors: What happens when you first turn on the voltage? Charges flow Current immediately starts to flow. from voltage It is largest at the start. 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

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. + 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

Capacitors: What happens when you first turn on the voltage? Meanwhile it starts to build a voltage. Charges flow from voltage The voltage starts out as vs and then grows. source It can’t change instantly. 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

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

What does a capacitor do to the current ? • 18

What does a capacitor do to the current ? • 19

What does a capacitor do to the current ? • 20

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

What does a capacitor do to the voltage ? • 22

Vs 66% at t=RC 23

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

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

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

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

Low Pass filter Noise Filter 28

Integrator http: //www. piclist. com/images/www/hobby_elec/e_ckt 1. htm 29

High Pass Filter DC Block 30

Differentiator 31 http: //www. piclist. com/images/www/hobby_elec/e_ckt 1. htm

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