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Capacitance

Capacitance. Physics 102 Professor Lee Carkner Lecture 13. sign of D U. sign of D V. sign of W. naturally?. + charge moves with E field. + charge moves against E field. -charge moves with E field. -charge moves against E field. PAL #12 Electric Potential. -. -. +. Yes. -. +.

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Capacitance

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  1. Capacitance Physics 102 Professor Lee Carkner Lecture 13

  2. sign of DU sign of DV sign of W naturally? + charge moves with E field + charge moves against E field -charge moves with E field -charge moves against E field PAL #12 Electric Potential - - + Yes - + + No + - - No - + + Yes

  3. Particle Motion E Decrease U (natural) Increase U High V Increase U Decrease U (natural) Low V

  4. If a charge of value Q is at a point of potential V, we know, • The velocity of the charge at that point • The direction the charge will move in • The amount of electrical potential energy the charge has • The distance to the nearest other charge • None of the above

  5. If a charged particle moves along an equipotential line (assuming no other forces), • Its potential energy does not change • No work is done • Its kinetic energy does not change • Its velocity does not change • All of the above

  6. When a charge +Q is placed at the corner of a square the potential at the center is 3 volts. What is the potential at the center if charges of +Q are placed on all corners of the square? • 0 V • 3 V • 9 V • 12 V • 24 V

  7. Circuits • What is the purpose of potential difference? • It makes charges move • e.g. light lightbulbs, induce movement in motors, move information etc. • We will examine the key components of electric circuits • Up first, the capacitor

  8. Capacitance • A capacitor is a device that can store charge and thus energy • The amount of charge depends on the potential difference across the capacitor and the intrinsic properties of the device • This intrinsic property is called capacitance and is represented by C

  9. Capacitance Defined • The amount of charge stored by a capacitor is just: • Or, defining the capacitance: C = Q/DV • The units of capacitance are farads (F) 1 F = 1 C/V • Typical capacitances are much less than a farad: • e.g. microfarad = mF = 1 X 10-6 F

  10. Capacitor Info • Maintaining a potential difference across the plates causes the charge to separate • Electrons are repelled from the negative terminal and end up on one plate • Plates have a net charge • Plates can’t touch or charge would jump across

  11. Capacitor Diagram - - Q DV DV + +

  12. Capacitor Properties • The capacitance depends on four things: • The distance between them (d) • The dielectric constant of the material between the plates (k) • The permittivity of free space (e0) • A constant: e0 = 8.85 X 10-12 C2/N m2 • The total capacitance can be written as: C = ke0(A/d)

  13. Capacitance Dependences

  14. Dielectric • The molecules in the material will align with the electric field • The polarized material partially cancels out the electric field between the plates reducing the voltage • A dielectric allows a capacitor to store more charge with the same voltage

  15. Dielectrics

  16. Dielectric Constant • The dielectric constant is a multiplicative factor for the capacitance • C = kC0 • e.g. • The dielectric also allows you to move the plates closer together without touching

  17. Breakdown • The dielectric must be an insulator • If the voltage is large enough, the charge will jump across anyway • While Q = CV, there is a limit to how much we can increase Q by increasing V • Normally about 20 million volts

  18. Energy in a Capacitor • Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch • Charge stops moving when the DV across the plates is equal to the max DV possible for the circuit

  19. Charging a Capacitor

  20. Total Energy • We find that the total energy stored in a capacitor is related to the charge and the final potential difference: Energy = 1/2 Q DV =1/2 C (DV)2 = Q2/2C • Large C and large DV produce large stored energy

  21. Using Capacitors • Generally only for short periods of time • Charge can bleed-off if capacitor is not perfectly insulated and potential is not maintained • Useful when you need a quick burst of energy • For a flash, capacitor is discharged into a gas (like xenon) that will glow when ionized • Since capacitance depends on d, can also use capacitance to measure separation

  22. Next Time • Read 18.1-18.5, 18.8-18.9 • Homework Ch 17, P: 44, 49, Ch 18, P: 4, 26

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