Capacitors and Capacitance PDF

Capacitors and Capacitance  A capacitor is an electronic component that stores energy in the form of an electrostatic field. In its simplest form, a capacitor consists of two conducting plates separated by an insulating material called the dielectric. In circuit diagrams a capacitor is rep...

Capacitors and Capacitance  A capacitor is an electronic component that stores energy in the form of an electrostatic field. In its simplest form, a capacitor consists of two conducting plates separated by an insulating material called the dielectric. In circuit diagrams a capacitor is represented by either of these symbols:  Evolution in Capacitors Film dielectrics “Wet” electrolytic capacitors Ceramic Capacitors Polymer Capacitors http://www.capacitorlab.com/capacitor-types-polymer/ Capacitors and capacitance Any two conductors separated by an “insulator” form a capacitor. Insulator will allow E field between the conductors, Insulator will not allow charge to flow from one conductor through itself to the other. The more charge you can hold, the larger the capacitor! “capacity” Charge a capacitor by pushing it there with a potential voltage “pressure” Capacitors and capacitance Units of Capacitance: [Coulombs/Volt] = FARADs But [Volt] = [Joules/Coulomb] Farads = Coulombs2/Joule  Capacitors and capacitance The definition of capacitance is C = Q/Vab. – Q = “charge stored” – Q is held symmetrically (same +Q as –Q) – Vab = pressure that pushes and keeps charge there – C increases as Q increases more capacity! – C decreases as Vab increases more pressure required to hold the charge there, so less effective in storing it temporarily!  Capacitors and capacitance - Capacitance depends only on the shapes, sizes, and relative positions of the conductors and on the nature of the insulator between them. - For special types of insulating materials, the capacitance does depend on Q and Vab.  Parallel-plate capacitor – TWO parallel conducting plates – Separated by distance that is small compared to their dimensions.  Parallel-plate capacitor – The capacitance of a parallel-plate capacitor is C = 0A/d  Parallel-plate capacitor – The capacitance of a parallel-plate capacitor is C = 0A/d. – Note! C is engineered! You control Area & distance by design! – C increases with Area – C decreases with separation Example The parallel plates of a 1.0-F capacitor are 1.0 mm apart. What is their area?  Parallel-plate capacitor Example The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00 m2 in area. A 10.0-kv potential difference is applied across the capacitor. Compute (a) the capacitance; (b) the charge on each plate; and (c) the magnitude of the electric field between the plates.  Energy stored in a capacitor U increases with more stored charge; U is less for fixed charge on a larger capacitor U = Q2/2C but C = Q/V…. so U = 1/2 QV. U = Q2/2C and Q = CV … so U = 1/2 CV2  Dielectrics Dielectric is nonconducting material. Most capacitors have dielectric between plates. Dielectric increases the capacitance and the energy density by a factor K. Dielectric constant of material is K = C/C0 > 1. Dielectric reduces E field between the plates. Dielectric reduces VOLTAGE between plates w/ fixed Q on each.  The Dielectric Constant (κ) - of a substance is a measure of how effective it is in reducing an electric field set up across a sample of it - for a capacitor, reducing E means reducing V as well. where Eo = electric field of a capacitor without a dielectric E = electric field of a capacitor with a dielectric Table 24.1—Some dielectric constants Amount of charge stored in a capacitor with dielectric A – area of capacitor plates d – distance between capacitor plates V – voltage K – dielectric constant Capacitance of a Parallel-plate capacitor filled with a dielectric Which means that A (which depends on the geometry of the capacitor), d, and K affect capacitance And potential difference between the plates is V = Ed Problems: 1. What voltage is required to store 7.2 x 10-5 C of charge on the plates of a 6-µF capacitor? 2. The electric potential energy stored in the capacitor of a defibrillator is 73 J and the capacitance is 120 µF. What is the voltage across the capacitor? 3. A parallel plate capacitor has a capacitance of 7.0 µF when filled with a dielectric. The area of each plate is 1.5 m2 and the separation between the plates is 1.0 x 10-3 m. What is the dielectric constant of the dielectric? 4. What is the potential difference between the plates of a 3.3-F capacitor that stores sufficient energy to operate a 75-watt light bulb for 1 minute? References: Cutnell, Johnson, Young, & Staedler (2012).Cutnell & Johnson Physics, 10th ed. John Wiley & Sons, Inc. Walker (2014). Halliday & Resnick Fundamentals of Physics 10th ed. Wiley & Sons,Inc. Young & Freedman (2016). University Physics 14th ed. Pearson Education, Inc/