GOVERNMENT ENGINEERING COLLEGE GODHRA 5TH SEM ELECTRONICS & COMMUNICATION 130600111021 130600111022 130600111027 130600111028 130600111029

Topic:- Capacitance

Capacitance The capacitance C of a conductor is defined as the ratio of the charge Q on the conductor to the potential V produced. Earth Battery Conductor - e- Q, V Capacitance:

Capacitance in Farads One farad (F) is the capacitance C of a conductor that holds one coulomb of charge for each volt of potential. Example: When 40 mC of charge are placed on a con- ductor, the potential is 8 V. What is the capacitance? C = 5 mF

To control variation time scales in a circuit Capacitance: To store charge To store energy To control variation time scales in a circuit

Capacitance and Shapes The charge density on a surface is significantly affected by the curvature. The density of charge is greatest where the curvature is greatest. + + Leakage (called corona discharge) often occurs at sharp points where curvature r is greatest.

Capacitance: When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: q+ and q-. However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates. The charge q and the potential difference V for a capacitor are proportional to each other: The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The SI unit is called the farad (F): 1 farad (1 F)= 1 coulomb per volt =1 C/V.

Charging a Capacitor: The circuit shown is incomplete because switch S is open; that is, the switch does not electrically connect the wires attached to it. When the switch is closed, electrically connecting those wires, the circuit is complete and charge can then flow through the switch and the wires. As the plates become oppositely charged, that potential difference increases until it equals the potential difference V between the terminals of the battery. With the electric field zero, there is no further drive of electrons. The capacitor is then said to be fully charged, with a potential difference V and charge q.

Calculating the Capacitance:

Calculating the Capacitance; A Cylindrical Capacitor : As a Gaussian surface, we choose a cylinder of length L and radius r, closed by end caps and placed as is shown. It is coaxial with the cylinders and encloses the central cylinder and thus also the charge q on that cylinder.

Calculating the Capacitance; A Spherical Capacitor:

Now letting b→∞, and substituting R for a, Calculating the Capacitance; An Isolated Sphere: We can assign a capacitance to a single isolated spherical conductor of radius R by assuming that the “missing plate” is a conducting sphere of infinite radius. The field lines that leave the surface of a positively charged isolated conductor must end somewhere; the walls of the room in which the conductor is housed can serve effectively as our sphere of infinite radius. To find the capacitance of the conductor, we first rewrite the capacitance as: Now letting b→∞, and substituting R for a,

Parallel Plate Capacitance d Area A +Q -Q For these two parallel plates: You will recall from Gauss’ law that E is also: Q is charge on either plate. A is area of plate. And

Capacitors in Parallel:

The Permittivity of a Medium The capacitance of a parallel plate capacitor with a dielectric can be found from: The constant e is the permittivity of the medium which relates to the density of field lines.

Capacitors in Series:

Energy 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

Energy Stored in an Electric Field:

Energy Density for Capacitor Energy density u is the energy per unit volume (J/m3). For a capacitor of area A and separation d, the energy density u is found as follows: Energy Density u for an E-field: A d Energy Density u:

Applications of Capacitors A microphone converts sound waves into an electrical signal (varying voltage) by changing d. d Changing d Microphone + - A Variable Capacitor Changing Area The tuner in a radio is a variable capacitor. The changing area A alters capacitance until desired signal is obtained.

Summary of Formulas

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