1 / 24

Ch.26: Capacitance and Dielectrics.

Ch.26: Capacitance and Dielectrics. Early History Applications Related equations Capacitor Networks. Charges in space set-up Electric Field. Fields can do work. Why? __________ ________________.

cheung
Download Presentation

Ch.26: Capacitance and Dielectrics.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Ch.26: Capacitance and Dielectrics. • Early History • Applications • Related equations • Capacitor Networks LNK2LRN

  2. Charges in space set-up Electric Field. Fields can do work. Why? __________ ________________ E = F/q , F = qE E = kQ/d2 , W = qEd , W/q = Ed , V = Ed , V = kQ/d , and W = qV Opposite charges insulated from one another form a CAPACITOR. LNK2LRN

  3. Early History of Capacitors. Galvanism: In 1800, produced electrical current from the contact of two different metals in a moist environment. Luigi Galvani (1737-1798)  Frog-leg experiment. LNK2LRN

  4. In 1799, metal discs (zinc with copper or silver) , separated with paperboard discs soaked in saline solution. This stack was the first electric battery. Alessandro Giuseppe Volta (1745-1827) The Voltaic Pile. LNK2LRN

  5. In 1810, Davy uses the Voltaic Pile to begin electrochemistry. Isolated elemental K, Ca, Ba, Na, Sr, Mg, B, and Si. His lab assistant was Michael Faraday! Considered his greatest discovery. Sir Humphry Davy (1778-1829)Founder of Electrochemistry. LNK2LRN

  6. Michael Faraday (1791-1867) discovered variable capacitor. Later, the SI unit used for capacitance was named a Farad (F) in his honor. 1F = 1 C / V In words: one Farad is equal to one Coulomb per Volt LNK2LRN

  7. Capacitance • Capacitance is the ability of a conductor to store energy in the form of electrically separated charges. LNK2LRN

  8. Capacitance • Capacitance is the ratio of charge to potential difference. Q C = ΔV LNK2LRN

  9. A parallel plate capacitor before charging. There is no net charge on the plates. LNK2LRN

  10. During charging, the negative charges will move to one plate. Now, each plate has a small charge. LNK2LRN

  11. After charging, each plate has a larger net charge, which it can hold even after the battery is gone. LNK2LRN

  12. Farads • Capacitance is measured in units called farads (F). • 1 farad = 1 coulomb/1 volt • Common measures are in microfarads (mF) and picofarads (pF = 1 x 10-12 F). • Named for Michael Faraday (1791-1867), a prominent British physicist. LNK2LRN

  13. Capacitance depends on: • Size and shape of capacitor. • Material between the plates. LNK2LRN

  14. Size and shape of the capacitor: If no material is between the plates of a capacitor (has to be in a vacuum), then the formula for capacitance is A C = εo d LNK2LRN

  15. Permittivity of free space: The Greek letter epsilon, e, represents a material-dependent constant called the permittivity of the material. When it is followed by a subscripted o, it is called the permittivity of free space, and has a value of 8.85 x 10-12 C2/N. m2 LNK2LRN

  16. Capacitance Example How much charge is on a 1 F capacitor which has a potential difference of 110 Volts? Q = CV = (1)(110) = 110 Coulombs How much energy is stored in this capacitor? Ecap = QV/2 = (110) (110) / 2 = 6,050 Joules! LNK2LRN

  17. Parallel Plate CapacitorExample C = e0A/d Calculate the capacitance of a parallel plate capacitor made from two large square metal sheets 1.3 m on a side, separated by 0.1 m. A A d LNK2LRN

  18. 1 / Ceq = 1 / C1 + 1 / C2 (a) Two capacitors in series, (b) Same CHARGE different VOLTAGE. LNK2LRN

  19. Ceq = C1 + C2+C3 ··· Cn (a) Capacitors in parallel, (b) Same VOLTAGE different CHARGE. LNK2LRN

  20. Capacitance without dielectric Dielectric • Placing a dielectric between the plates increases the capacitance. • C = k C0 Dielectric constant (kappa) (k > 1) Capacitance with dielectric LNK2LRN

  21. Dielectric Constant, Strength • Large capacitance (energy storage) • Small gap (d) • Breakdown voltage is material dependent • Large area (A) • Would like to keep the device size tolerable • Large dielectric constant (ke0) • Large dielectric strength • Dielectric constant/strength of material LNK2LRN

  22. Capacitors can store charge and ENERGYDU = q DV, and the potential V increases as the charge is placed on the plates (V = Q / C). Since the V changes as the Q is increased, we have to integrate over all the little charges “dq” being added to a plate: DU = q DV leads to U = ò V dq = ò q/c dq = 1/C ò q dq = Q2 / 2C. And using Q = C V, we get U = Q2 / 2C = C V2 / 2 = Q V / 2So the energy stored in a capacitor can be thought of as the potential energy stored in the system of positive charges that are separated from the negative charges, much like a stretched spring has potential energy associated with it. LNK2LRN

  23. ELECTRIC FIELD ENERGY Here's another way to think of the energy stored in a charged capacitor: If we consider the space between the plates to contain the energy (equal to 1/2 C V2) we can calculate an energy DENSITY (Joules per volume). The volume between the plates is area x plate separation, or A d. Then the energy density u is u = 1/2 C V2 / A d = eo E2 / 2 Recall C = eo A / d and V =E d. LNK2LRN

  24. Energy density: u = eo E2 / 2 This is an important result because it tells us that empty space contains energy if there is an electric field (E) in the "empty" space. If we can get an electric field to travel (or propagate) we can send or transmit energy and information through empty space!!! LNK2LRN

More Related