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Transcript
Introduction to Electrical & Computer Engineering Capacitors Dr. Cynthia Furse University of Utah 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 C A d -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 accumulate on the top plate + + + + + + + + + + + Note: This creates a voltage + a ++ ++ Air (no charges) b The charges can’t cross the T. airUlaby space, because Circuits, Second Edition by Fawwaz and Michel itM. Maharbiz, © NTS is Publisher an open circuit, R = ∞ Press, Used with Permission by the Capacitors: Where is the current? Current = flow of charges I = dq/dt + Charges accumulate on the top plate + + + + + + ++ - + ++ + + Note: This creates a voltage + 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 – Icharges on the bottom plate = dq/dt Capacitors: Where does this mean? C = ɛA/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 = ɛA/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 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 from voltage It is largest at the start. source towards capacitor flow. + + + 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 Charges flow from voltage The voltage starts out as source It can’t change towards capacitor + + + build a voltage. vs and then grows. instantly. 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 + Charges accumulate on the top plate + + + + + + ++ - + ++ + + Note: This creates a voltage + 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_ckt1.htm 29 High Pass Filter DC Block 30 Differentiator 31 http://www.piclist.com/images/www/hobby_elec/e_ckt1.htm Introduction to Electrical & Computer Engineering Antelope Island, Great Salt Lake, Utah Dr. Cynthia Furse University of Utah 32