Basic Electrical QuantitiesBasic Electrical Quantities

CapacitanceCapacitance

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

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Some Capacitors

insulatorconductor

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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

Difference PotentialCharge

VQC

Hence, Capacitance is the charge required per unit Potential Difference

Parallel Plate Capacitor

V E

+Q

-Q-

+

VEdV

V E+Q

-Q-

+

VdEV

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 (106 ) or picofarad (1012 ) 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(-)

+ _

IA 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

EDielectric constant

Separation d

Area A +Q

V

Parallel-Plate Capacitor

0 0 0

. . .

aE dl dl a dlz d z d z d

zz

z z z

Q QVA A

Area A -Q

dl E d

Area A+Q

ââzz

aE from Gauss's LawzQA

QdVA

Q ACV d

Basic Electrical QuantitiesBasic Electrical Quantities

Capacitance in Series Capacitance in Series & Parallel& Parallel

Series Combination

21

21

QQQVVV

22

22

11

11

CQ

CQV

CQ

CQV

1 2eq

Q Q QVC C C

21

111CCCeq

n

j jeq CC 1

11For series capacitors

Parallel Combination

VCVCQVCVCQ

2222

1111

21

21

VVVQQQ

1 1 2 2

1 2 eqQ C V C V C V

C V C V

21 CCCeq

For parallel capacitors

n

jjeq CC

1

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 inductanceNL=

I

N= turns in a coil = flux produced I= current produced in a coil

where

If NΦ=1 Wb-turn and I= 1 ampere, then L= 1 HenryHence 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

AB sE E ir

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

( ) ( ) for any ( )t sv t v t i t 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)

+

-

vs(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

ABsEi IR

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( ) ( ) for any ( )si t i t v t

The current source is completely specified by its current is(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)

+

-

is(t)