Theory of Electricity

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THEORYOFELECTRICITY

MOLECULE: ALL MATTERS WHETHERSOLID, LIQUID OR GASEOUS CONSISTSOF MINUTE PARTICLES CALLEDMOLECULES.

ATOM: THE MOLECULES WHICH ARETHEMSELVES MADE UP OF STILL MINUTEPARTICLES KNOWN AS ATOMS.

ELEMENTS: THOSE SUBSTANCES WHOSE

MOLECULES CONSIST OF SIMILAR ATOMSARE KNOWN AS ELEMENTS.

COMPOUNDS: THOSE SUBSTANCESWHOSE MOLECULES CONSIST OF DIS-

SIMILAR ATOMS ARE CALLED


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THEORYOF ELECTRICITY MODERN THEORY INDICATES THAT

ATOMS OF ALL SUBSTANCES AREBUILT UP OF POSITIVE ELECTRICITYCALLED PROTONS, NEGATIVEELECTRICITY CALLED ELECTRONSAND NEUTRONS WHICH SHOW NOELECTRICAL STATE.

AN ATOM CONSISTS OF A CENTRALNEUCLEUS MADE UP OF PROTONSAND NEUTRONS AND AROUND THIS

NEUCLEUS THERE IS A NUMBER OFELECTRONS REVOLVING IN ORBITS:


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THEORYOF ELECTRICITY

IN THE NORMAL STATE, THENUMBER OF PROTONS EQUALS

THE NUMBER OF ELECTRONSAND THE ATOM AS A WHOLE ISELECTRICALLY UNCHARGED. i.e.

IT IS NEUTRAL. THE CONTINUOUS FLOW OF

ELECTRONS CONSTITUTE ANELECTRIC CURRENT.


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THEORYOF ELECTRICITY

THOSE SUBSTANCES WHOSEATOMS HAVE THEIR OUTERMOSTORBITS INCOMPLETE ACT AS GOOD

CONDUCTORS OF ELECTRICITY. i.e.THEY PERMIT AN EASYDETACHMENT OF THEIROUTERMOST ELECTRONS AND

OFFER VERY LITTLE HINDRANCETO THEIR FLOW THROUGH THEIRATOMS. SUCH SUBSTANCES ARE

KNOWN AS GOOD CONDUCTORS.


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THEORYOF ELECTRICITY RESISTANCE: RESISTANCE MAY BE

DEFINED AS THAT PROPERTY OF ASUBSTANCE WHICH OPPOSES THEFLOW OF ELECTRICITY THROUGH IT.ALL SUBSTANCES MAY BE BROADLY

DIVIDED INTO TWO CLASSES:- CONDUCTORS: THOSE SUBSTANCES

WHICH OFFER SUCH A SMALL

RESISTANCE THAT THEY READILYALLOW ELECTRICITY TO FLOWTHROUGH THEM.

INSULATORS: THOSE SUBSTANCES

WHICH OFFER SUCH ENORMOUS


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LAWS OF RESISTANCE

1. THE RESISTANCE OF ACONDUCTOR VARIES DIRECTLYAS ITS LENGTH.

2. THE RESISTANCE OF ACONDUCTOR VARIESINVERSELY AS ITS CROSS-

SECTION. 3. THE RESISTANCE OF A

CONDUCTOR DEPENDS ON THE


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FORMULA FOR CALCULATINGRESISTANCE

FROM LAWS (1) AND (2) ABOVE:

R L and R L

A

Tf R L

A

Hence, R = L where (rho) is a

constant forA

The material called its SPECIFICRESISTANCE or RESISTIVITY


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EFFECT OF TEMPERATURE ONRESISTANCE

1. PURE METALS INCREASE INRESISTANCE WITH RISE IN TEMPERATURE.

2. ALLOYS: MOST ALLOYS INCREASE VERYSLIGHTLY IN RESISTANCE WITH RISE INTEMPERATURE. THE RESISTANCE ALLOYSUSED IN ELECTRICAL WORK HAVE APRACTICALLY CONSTANT RESISTANCE ATALL TEMPERATURES.

3. CARBON, INSULATORS AND

ELECTROLYTES DECREASE IN RESISTANCEWITH RISE IN TEMPERATURE. (ANELECTROLYTE IS A SOLUTION WHICHCONDUCTS ELECTRICITY. Eg. WATER

CONTAINING SULPHURIC ACID.) THERESISTANCE OF AN INSULATOR


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TEMPERATURE CO-EFFICIENT

FOR PURE METALS AND ALLOYSTHE RESISTANCE / TEMPERATUREGRAPH IS PRACTICALLY ASTRAIGHT LINE, WITH INORDINARY LIMITS OFTEMPERATURE, SAY Oc to 100c.IF A RESISTOR HAS A VALUE R

at Oc, THEN AT 1c IT WILLINCREASE BY A SMALL AMOUNT. THE FRACTION CALLED


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SOURCES OFELECTRICITY

1. FROM CHEMICAL ENERGY BATTERIES

2. FROM ELECTRO-MAGNETISM GENERATOR

3. FROM SOLAR ENERGY

4. FROM NEUCLEAR ENERGY


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EFFECT OF ELECTRICCURRENT

1. PHYSICAL EFFECT

2. X RAY EFFECT

3. HEATING EFFECT 4. CHEMICAL EFFECT

5. MAGNETIC EFFECT


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OHMS LAW

OHMS LAW STATES THAT THECURRENT FLOWING THROUGH ASOLID CONDUCTOR AT CONSTANTTEMPERATURE IS DIRECTLY

PROPORTIONAL TO THE POTENTIALDIFFERENCE ACROSS THECONDUCTOR AND INVERSELYPROPORTIONAL TO ITS

RESISTANCE.I V and I 1 or I = V x

constant

R R


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LIMITATIONS OF OHMSLAW

OHMS LAW IS NOT APPLICABLE UNDER THE

FOLLOWING CONDITIONS:1. FOR METALS WHICH GET HEATED UP DUE

TO FLOW OF CURRENT THROUGH THEM.2. FOR ELECTROLYTES WHERE ENORMOUS

GASES ARE PRODUCED ON EITHERELECTRODE.3. FOR VACUUM RADIO VALVES4. FOR ARC LAMPS

5. FOR SEMI-CONDUCTORS6. FOR GAS FILLED TUBES, IN WHICH THEIONS ARE GENERATED AS A RESULT OFCURRENT FLOW.

7. FOR APPLIANCES SUCH AS METALRECTIFIERS AND CRYSTAL DETECTORS IN


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ELECTRICAL UNITSCURRENT: THE UNIT OF CURRENT IS

THE AMPERE(I). IT IS THE CONSTANTCURRENT WHICH, WHEN MAINTAINEDIN TWO PARALLEL STRAIGHTCONDUCTORS OF INFINITE LENGTHAND NEGLIGIBLE COSS-SECTIONSEPARATED BY A DISTANCE OF ONEMETER IN VACUO, PRODUCESBETWEEN THESE CONDUCTORS AFORCE EQUAL TO 2 x 10 -7NEWTONS PERMETRE LENGTH.

ONE AMPERE OF OF CURRENT IS SAID TOFLOW THROUGH THE CONDUCTOR, IF 628 x10 16ELECTRONS


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ELECTRICAL UNITS

THE POTENTIAL DIFFERENCE(VOLT) AND

ELECTROMOTIVE FORCE (e.m.f.):

THE DIFFERENCE OF POTENTIALBETWEEN TWO POINTS IN ACIRCUIT IS THE ELECTRICALPRESSURE OR VOTAGE REQUIREDTO DRIVE THE CURRENTBETWEEN THEM. THE VOLT ISTHEREFORE DEFINED AS THE p.d.

ACROSS A RESISTANCE OF ONE


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ELECTRICAL UNITS

RESISTANCE: RESISTANCE MAY BEDEFINED AS THE PROPERTY OF ASUBSTANCE DUE TO WHICH IT

OPPOSES THE FLOW OFELECTRICITY THROUGH IT.

THE UNIT OF RESISTANCE ISOHM.

A CONDUCTOR IS SAID TO HAVE ARESISTANCE OF ONE OHM IF ITPERMITS ONE AMPERE CURRENT

TO FLOW THROUGH IT WHEN


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RESISTANCE IN SERIESTHE CIRCUIT IN WHICH RESISTANCES

ARE CONNECTED END TO END SOTHAT THERE IS ONLY ONE PATH FORCURRENT FLOW IS CALLED A SERIESCIRCUIT.

IN A SERIES CIRCUIT:

1. THE SAME CURRENT FLOWSTHROUGH ALL THE RESISTANCES.

2. THERE WILL BE VOLTAGE DROPACROSS EACH RESISTANCE GIVEN BYOHMS LAW.

3. THE SUM OF THE VOLTAGE DROPS IS

RESISTANCE IN


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RESISTANCE INPARALLELTHE CIRCUIT IN WHICH ONE END OF EACH

RESISTANCE IS JOINED TO A COMMON POINT

AND THE OTHER END OF EACH RESISTANCE ISJOINED TO ANOTHER COMMON POINT SO THAT,THERE ARE AS MANY PATHS FOR CURRENTFLOW AS THE NUMBER OF RESISTANCES ISCALLED A PARALLEL CIECUIT.

IN PARALLEL CIRCUIT:

1.THE VOLTAGE ACROSS EACH RESISTANCE OFTHE PARALLEL COION IS THE SAME.MBINAT

2.THERE ARE AS MANY CURRENT PATHS AS THE

NUMBER OF BRANCHES.3.THE CURRENT IN EACH BRANCH IS GIVEN BY

OHMS LAW AND THE TOTAL CURRENT ISEQUAL TO THE SUM OF BRANCH CURRENTS.

I = I + I + I. 1 = 1 + 1


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ELECTRICAL POWER

IT IS EXPRESSED IN TERMS OFWATTS (WATT) AND ISGIVEN BY :

E x I = I R = ER

POWER IS USUALLY EXPRESSED INTERMS OF :

KW ( KILOWATTS ) (= 1000WATTS) or


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KIRCHHOFFS LAWS

THESE LAWS ARE MORE COMPREHENSIVETHAN OHMS LAW AND ARE USED FORSOLVING ELECTRICAL NETWORKSWHICH MAY NOT BE READILY SOLVED

BY THE LATER.KIRCHHOFFS LAWS, TWO IN NUMBERS,

ARE PARTICULARLY USEFUL:

A)IN DETERMINING THE EQUIVALENTRESISTANCE OF A COMPLICATEDNETWORK OF CONDUCTORS.

B) FOR CALCULATING THE CURRENTS

FLOWING IN THE VARIOUS


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POINT LAW or CURRENTLAW

1) IN ANY ELECTRICAL NETWORK,THE ALGEBRAIC SUM OF THECURRENTS MEETING AT A POINT

(or JUNCTION) IS ZERO.PUT IN ANOTHER WAY, IT SIMPLY

MEANS THAT THE TOTAL CURRENT

LEAVING A JUNCTION IS EQUAL TOTHE TOTAL CURRENT ENTERINGTHAT JUNCTION.

IT IS OBVIOUSLY TRUE BECAUSETHERE IS NO ACCUMULATION OR


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POINT LAW or CURRENTLAW

I + (-I) + (-I) + (+I) +(-I) = 0

or I + I - I - I - I = 0

or I + I = I + I + Ior

INCOMING CURRENTS =OUTGOING CURRENTS

SIMILARLY, IN FIG (b):

+ I + ( - I) + ( - I) + ( - I)+ ( - I) = O

or I = I + I + I + I

MESH LAW VOLTAGE


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MESH LAW or VOLTAGELAW

IT STATES: THE ALGEBRAIC SUM OF THE

PRODUCTS OF CURRENTS ANDRESISTANCES IN EACH OF THECONDUCTORS IN ANY CLOSED PATH ( orMESH) IN A NETWORK PLUS THEALGEBRAIC SUM OF THE e.m.fsIN THATPATH IS ZERO.INOTHER WORDS, IR + e.m.f =O.

IT SHOULD BE NOTED THAT ALGEBRAICSUM IS THE SUM WHICH TAKES INTOACCOUNT THE POLARITIES OF THEVOLTAGE DROPS. Also:

IN ANY CLOSED PATH IN A NETWORK, THE


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DETERMINATION OFVOLTAGE SIGN

IN APPLYING KIRCHHOFFS LAWSTO SPECIFIC PROBLEMS,PARTICULAR ATTENTION SHOULD

BE PAID TO THE ALGEBRAICSIGNS OF VOLTAGE DROPS ANDe.m.f.s. OTHERWISE RESULTS

WILL COME OUT TO BE WRONG.


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SIGN OF BATTERY E.M.F.A RISE IN VOLTAGE SHOULD BE GIVEN

A + SIGN AND A FALL IN VOLTAGE ,A SIGN. KEEPING THIS IN MIND, ITIS CLEAR THAT AS WE GO FROM THE ve TERMINAL OF A BATTERY TO ITS +

ve TERMINAL, THERE IS A RISE INPOTENTIAL. HENCE, THIS VOLTAGESHOULD BE GIVEN A + ve SIGN. IF,ON THE OTHERHAND, WE GO FROM +

ve TERMINAL TO ve TERMINAL,THEN THERE IS A FALL INPOTENTIAL. HENCE, THIS VOLTAGESHOULD BE PROCEEDED BY A veSIGN. IT IS IMPORTANT TO NOTETHAT THE SIGN OF THE BATTERY


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SIGN OF IR DROPSNOW, TAKE THE CASE OF A RESISTOR. IF WE GO

THROUGH A RESISTOR IN THE SAME DIRECTIONAS THE CURRENT, THEN THERE IS A FALL INPOTENTIAL BECAUSE CURRENT FLOWS FROM AHIGHER TO A LOWER POTRENTIAL. HENCE,THIS VOLTAGE FALL SHOULD BE TAKEN ve.HOWEVER, IF WE GO IN A DIRECTIONOPPOSITE TO THAT OF THE CURRENT, THENTHERE IS A RISE IN VOLTAGE. HENCE, THISVOLTAGE RISE SHOULD BE GIVEN A +ve SIGN.

IT IS CLEAR THAT THE SIGN OF VOLTAGE DROPACROSS A RESISTOR DEPENDS ON THEDIRECTION OF CURRENT THROUGH THATRESISTOR BUT IS INDEPENDENT OF THEPOLARITY OF ANY OTHER SOURCE OF e.m.f IN

THE CIRCUIT UNDER CONSIDERATION.


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SIGN OF IR DROPS

I R is ve. (Fall in potential)I R is ve. (Fall in potential)

I R is +ve. (Rise in potential)

I R is ve. (Fall in potential)E is ve. (Fall in potential)

E is + ve. (Rise in potential)

Using KIRCHHOFFS VOLTAGE LAW,we get:

-IR - IR + IR - IR - E + E = O(or)


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TWELVE FORMULAE:

VOLTAGE CURRENTRESISTANCE WATTS

V = I X R I = V R =

V W = I X VR

I

V = W I = W R =V W = I X R

I VW


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Theory of Electricity