Basic Electrical Quantities Capacitance

Capacitance  A capacitor is constructed of two parallel conducting plates separated by an insulator called dielectric  The conducting surfaces can be rectangular or circular  The purpose of the capacitor is to store electrical energy by electrostatic stress in the dielectric

ELECTRICAL SCIENCE Some Capacitors insulator conductor

ELECTRICAL SCIENCE Capacitance : Definition Take two chunks of conductor Separated by insulator Apply a potential V between them Charge will appear on the conductors, with Q + = +CV on the higher-potential and Q - = - CV on the lower potential conductor C depends upon both the “geometry” and the nature of the material that is the insulator 0 V Q+ = +CV Q- = -CV V

Parallel Plate Capacitor  When it is connected to a voltage source, there is temporary flow of electrons from plate A to plate B  A capacitor has a capacitance of 1 farad (F) if 1 coulomb (C) of charge is deposited on the plates by a potential difference of 1 volt across its plates  The farad is named after Michael Faraday, a nineteenth century English chemist and physicist

Capacitance  Capacitance is a measure of a capacitor’s ability to store charge on its plates  A capacitor has a capacitance of one farad (F) if one coulomb (C) of charge is deposited on the plates by a potential difference of one volt across its plates  The farad is named after Michael Faraday, a nineteenth century English chemist and physicist

Capacitance Suppose we give Q coulomb of charge to one of the two plates and if a P.D. of V volts is established between the two plates, then the capacitance is  Hence, Capacitance is the charge required per unit Potential Difference

Parallel Plate Capacitor V E +Q -Q - + V E +Q -Q - + The potential difference between the battery terminals and the plates will create a field and charges will flow from the battery to the plates until the potential difference is zeroed. Capacitance is inversely proportional to the distance between the plates.

Capacitance  The farad is generally too large a measure of capacitance for most practical applications  So microfarad (10  6 ) or picofarad (10  12 ) is more commonly used  Different capacitors for the same voltage across their plates will acquire greater or lesser amounts of charge on their plates  Hence, the capacitors have greater or lesser capacitance

Parallel Plate Capacitor Charge Q(+) Charge Q(-) + _ I A B

Capacitance  Dielectric – Insulator of the capacitor  The purpose of the dielectric is to create an electric field to oppose the electric field setup by free charges on the parallel plates  Di for “opposing” and electric for “electric field”

Capacitance  With different dielectric materials between the same two parallel plates, different amounts of charge will deposit on the plates  Permittivity – The ratio of the flux density to the electric field intensity in the dielectric. A measure of how easily the dielectric will “permit” the establishment of flux lines within the dielectric

Parallel-Plate Capacitor 1. Calculate field strength E as a function of charge ±Q on the plates 2. Integrate field to calculate potential V between the plates 3. Q=CV, C = V/Q Area A -Q E Dielectric constant  Separation d Area A +Q V

Parallel-Plate Capacitor Area A-Q  dl E d Area A +Q âzâzâzâz

Basic Electrical Quantities Capacitance in Series & Parallel

Series Combination For series capacitors

Parallel Combination For parallel capacitors

Parallel Connections All are parallel connections This is not

Mixed Combination of Capacitors

Find the capacitance

Series and Parallel Key ideas: 1.For capacitors in series, the charges are all the same. 2.For capacitors in parallel, the potential differences are all the same.

Mixed Combination of Capacitors

Find the capacitance

Inductance Whenever a coil of wire is connected to a battery through a rheostat and effort is made to increase the current and hence flux through it, it is always opposed by the instantaneous production of counter emf. The energy required to oppose this is supplied by the battery Similarly if the current is decreased then again is delayed due to production of counter emf

Inductance This property of the coil due to which it opposes any increase or decrease of current or flux through it is known as inductance or Self inductance If NΦ=1 Wb-turn and I= 1 ampere, then L= 1 Henry Hence a coil is said to have self-inductance of one Henry if a current of one ampere when flowing through it produces flux linkages of one Wb-turn in it

Coefficient of Inductance It is defined as the Weber-turns per ampere in the coil It is quantitatively measured in terms of coefficient of self induction Symbol (L), Unit H (Henry) The property is analogous to inertia in a material body

Electrical Energy Sources

Classification of Sources Voltage Source Current Source Further sub classified as Ideal or Non-ideal Dependent or Independent Voltage Source Current Source

Voltage Source An ideal voltage source is a source of voltage with zero internal resistance (a perfect battery) Supply the same voltage regardless of the amount of current drawn from it

Voltage Source An non-ideal or real or practical voltage source has a small but finite resistance The terminal voltage delivered is less by an amount equaling the voltage drop caused by the internal resistance If r=0, then the source becomes Ideal Voltage Source

Independent Voltage Source An ideal voltage source is shown to be connected to an arbitrary network The defining equation is The voltage source is completely specified by its voltage for all t It does not depend on the connected network in any manner Such ideal voltage source is also called an Independent Voltage source Arbitrary Network i(t) + - v(t) + - v s (t)

Current Source An ideal current source is capable of producing a specified current through it regardless of what is connected to it The current supplied is independent of the voltage at the source terminals

Current Source An non-ideal or real or practical current source has a large but finite resistance If r=infinite, then the source becomes Ideal current Source

Independent Current Source An ideal current source is shown to be connected to an arbitrary network The defining equation is The current source is completely specified by its current i s (t) for all t It does not depend on the connected network in any manner Such ideal current source is also called an Independent current source Arbitrary Network i(t) + - v(t) + - i s (t)