2Maximum Charge on a Conductor A battery establishes a difference of potential that can pump electrons e- from a ground (earth) to a conductorEarthBatteryConductor-e-There is a limit to the amount of charge that a conductor can hold without leaking to the air. There is a certain capacity for holding charge.
3CapacitanceThe capacitance C of a conductor is defined as the ratio of the charge Q on the conductor to the potential V produced.EarthBatteryConductor-e-Q, VCapacitance:
4Capacitance in FaradsOne farad (F) is the capacitance C of a conductor that holds one coulomb of charge for each volt of potential.Example: When 40 μC of charge are placed on a conductor, the potential is 8 V. What is the capacitance?
5Capacitance of Spherical Conductor At surface of sphere:+QrE and V at surface.Capacitance, C
6Example 1: What is the capacitance of a metal sphere of radius 8 cm? r = 0.08 mCapacitance, C+QrNote: The capacitance depends only on physical para- meters (the radius r) and is not determined by either charge or potential. This is true for all capacitors.
7Example 1 (Cont.): What charge Q is needed to give a potential of 400 V? r = 0.08 mCapacitance, C+QrNote: The farad (F) and the coulomb (C) are extremely large units for static electricity. The SI prefixes micro μ, nano n, and pico p are often used.
9Example 3. The plates of a parallel plate capacitor have an area of 0 Example 3. The plates of a parallel plate capacitor have an area of 0.4 m2 and are 3 mm apart in air. What is the capacitance?3 mmdA0.4 m2
10Dielectric MaterialsMost capacitors have a dielectric material between their plates to provide greater dielectric strength and less probability for electrical discharge.+-AirCoEo+-Dielectricreduced E+-C > CoE < EoThe separation of dielectric charge allows more charge to be placed on the plates—greater capacitance C > Co.
11Dielectric constant: K = 1 for Air The dielectric constant K for a material is the ratio of the capacitance C with this material as compared with the capacitance Co in a vacuum.Dielectric constant: K = 1 for Air
12Energy of Charged Capacitor The potential energy U of a charged capacitor is equal to the work (qV) required to charge the capacitor.If we consider the average potential difference from 0 to Vf to be V/2:Work = Q(V/2) = ½QV
14Capacitors in Circuits Let’s start with the most basic circuit.Typically, we are solving for the charge on the capacitor and potential difference across the platesAt times, we will also be asked about the stored energy.
15Series Circuits The key here is - no choice Let’s find Q and ∆V for each capacitor.
16Series Circuits The key here is - no choice Let’s find Q and ∆V for each capacitor.
17Parallel Circuits The key here is - choice Let’s find Q and ∆V for each capacitor.
18Complex CircuitsThe key here is - make it look either like series or parallelLet’s find Q and ∆V for each capacitor.
19Complex CircuitsThe key here is - make it look either like series or parallelLet’s find Q and ∆V for each capacitor.