THE STORY OF PETER

THE STORY OF PETER King James Version: Acts Chapter 10 1 There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band, 2 A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway. 3 He saw in a vision evidently about the ninth hour of the day an angel of God coming in to him, and saying unto him, Cornelius. 4 And when he looked on him, he was afraid, and said, What is it, Lord? And he said unto him, Thy prayers and thine alms are come up for a memorial before God. 5 And now send men to Joppa, and call for one Simon, whose surname is Peter: 6 He lodgeth with one Simon a tanner, whose house is by the sea side: he shall tell thee what thou oughtest to do. 7 And when the angel which spake unto Cornelius was departed, he called two of his household servants, and a devout soldier of them that waited on him continually; 8 And when he had declared all these things unto them, he sent them to Joppa. 9 On the morrow, as they went on their journey, and drew nigh unto the city, Peter went up upon the housetop to pray about the sixth hour: 10 And he became very hungry, and would have eaten: but while they made ready, he fell into a trance, 11 And saw heaven opened, and a certain vessel descending upon him, as it had been a great sheet knit at the four corners, and let down to the earth: 12 Wherein were all manner of fourfooted beasts of the earth, and wild beasts, and creeping things, and fowls of the air. 13 And there came a voice to him, Rise, Peter; kill, and eat. 14 But Peter said, Not so, Lord; for I have never eaten any thing that is common or unclean. 15 And the voice spake unto him again the second time, What God hath cleansed, that call not thou common. 16 This was done thrice: and the vessel was received up again into heaven. 17 Now while Peter doubted in himself what this vision which he had seen should mean, behold, the men which were sent from Cornelius had made enquiry for Simon's house, and stood before the gate, 18 And called, and asked whether Simon, which was surnamed Peter, were lodged there. 19 While Peter thought on the vision, the Spirit said unto him, Behold, three men seek thee. 20 Arise therefore, and get thee down, and go with them, doubting nothing: for I have sent them. 21 Then Peter went down to the men which were sent unto him from Cornelius; and said, Behold, I am he whom ye seek: what is the cause wherefore ye are come? 22 And they said, Cornelius the centurion, a just man, and one that feareth God, and of good report among all the nation of the Jews, was warned from God by an holy angel to send for thee into his house, and to hear words of thee. 23 Then called he them in, and lodged them. And on the morrow Peter went away with them, and certain brethren from Joppa accompanied him. 24 And the morrow after they entered into Caesarea. And Cornelius waited for them, and he had called together his kinsmen and near friends. 25 And as Peter was coming in, Cornelius met him, and fell down at his feet, and worshipped him. 26 But Peter took him up, saying, Stand up; I myself also am a man. 27 And as he talked with him, he went in, and found many that were come together. 28 And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean. 29 Therefore came I unto you without gainsaying, as soon as I was sent for: I ask therefore for what intent ye have sent for me? 30 And Cornelius said, Four days ago I was fasting until this hour; and at the ninth hour I prayed in my house, and, behold, a man stood before me in bright clothing, 31 And said, Cornelius, thy prayer is heard, and thine alms are had in remembrance in the sight of God. 32 Send therefore to Joppa, and call hither Simon, whose surname is Peter; he is lodged in the house of one Simon a tanner by the sea side: who, when he cometh, shall speak unto thee. 33 Immediately therefore I sent to thee; and thou hast well done that thou art come. Now therefore are we all here present before God, to hear all things that are commanded thee of God. 34 Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons: 35 But in every nation he that feareth him, and worketh righteousness, is accepted with him. 36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:) 37 That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached; 38 How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him. 39 And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree: 40 Him God raised up the third day, and shewed him openly; 41 Not to all the people, but unto witnesses chosen before God, even to us, who did eat and drink with him after he rose from the dead. 42 And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead. 43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins. 44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. 45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. 46 For they heard them speak with tongues, and magnify God. Then answered Peter, 47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? 48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days. ACTS 10 AND ACTS 12 THE STORY OF CONELIUS ACTS 10:35 GOD IS NO RESPECTER OF PERSON BUT IN EVERY NATION EVERYONE WHO FEARS HIM AND DOES RIGHTEOUSNESS IS ACCEPTABLE UNTO HIM. GOD IS NO RESPECTER OF PERSONS BUT IN EVERY NATION HE THAT FEARETH HIM AND WORKETH RIGHTEOUSNESS, IS ACCEPTED WITH HIM. ACTS 10 VS 1 A CERTAIN MAN IN CEASAREA CALLED CORNELIUS A CENTURION OF THE BAND CALLED THE ITALIAN BAND. VS 2 A DEVOUT MAN AND ONE THAT FEARED GOD WITH ALL HIS HOUSE, WHICH GAVE MUCH ALMS TO THE PEOPLE, AND PRAYED TO GOD ALWAYS. THIS WAS A MAN JUST LIKE ANY OTHER MAN HE WAS A CENTURION. HE WAS A DEVOUT MAN AND HE FEARED GOD WITH ALL HIS HOUSE. HE ENSURED THAT HIS HOUSE FEARED GOD. PARENTS SHOULD ENSURE THAT THEY FEAR GOD WITH ALL THEIR HOUSE. HE GAVE MUCH ALMS TO THE PEOPLE AND PRAYED TO GOD ALWAYS. NOTICE THAT THIS MAN SPENT TIME IN PRAYER WITH GOD ALWAYS. HE ALSO GAVE MUCH ALMS TO THE PEOPLE. WHEN YOUSPEND TIME WITH GOD, IT IS EASIER TO DO GOOD TO MEN. GOD IS THE SOURCE OF ALL GOOD THINGS. IT IS IMPORTANT TO PRAY TO GOD ALWAYS. WHEN YOUR WAYS PLEASE THE LORD, HE WILL SEND YOU AN ANGEL WITH SPECIFIC INSTRUCTIONS AND BLESSING FOR YOU AND FOR YOUR SALVATION. VS 3 HE SAW A VISION ABOUT THE NINTH HOUR VS 4 -5 AN ANGEL OF GOD FROM GOD CALLED HIM AND HE ANSWERED THY PRAYERS AND THINE ALMS ARE COME UP FOR A MEMORIAL BEFORE GOD. EVERYTHING YOU DO IS RECORDED. GOD KNOWS ALL OUR ACTIVITIES. IT IS SIGNIFICANT THAT HE ANSWERED. WHEN GOD CALLS US WE SHOULD ANSWER WHEN JESUS CHRIST COMES CALLING WE SHOULD BE READY TO ANSWER THE CALL. REMEMBER THAT MANY ARE CALLED BUT FEW ARE CHOSEN. VS 5 HE WAS GIVEN INSTRUCTIONS. GOD GIVES INSTRUCTIONS TO THOSE WHOM HE CALLS BECAUSE THEY LOVE OUR LORD JESUS CHRIST AND OBEY HIM. NOW SEND MEN TO JOPPA AND CALL FOR ONE SIMON, WHOSE SURNAME IS PETER GOD’S INSTRUCTIONS ARE SPECIFIC. VS 8 WHEN YOU HAVE AN ENCOUNTER WITH GOD, PLEASE SPREAD THE GOOD NEWS. WHEN HE HAD DECLARED ALL THESE THINGS UNTO THEM, HE SENT THEM TO JOPPA. VS 9 PETER TOO HAD AN ENCOUNTER WITH GOD AND WAS GIVEN SPECIFIC INSTRUCTIONS, A VISION WITH A MEANING; RELEVANT TO THE TASK AHEAD. PETER WENT UP UPON THE HOUSE TOP TO PRAY ABOUT THE SIXTH HOUR. VS 10 HE BECAME VERY HUNGRY . JUST LIKE ANY BODY ELSE, CHRISTIANS BECOME HUNGRY. ------ ---- AND WOULD HAVE EATEN BUT WHILE THEY MADE READY, HE FELL INTO A TRANCE. VS 11 – 16 THE ACCOUNT OF THE VISION: PETER KILL AND EAT. WHAT GOD HATH CLEANSED, THAT CALL NOT HOU COMMON. THIS HAPPENED THREE TIMES. THE JEWS WERE GIVEN SPECIFIC INSTRUCTIONS ABOUT THEIR DIETS . CERTAIN FOOD ITEMS WERE FORBIDEN AND CONSIDERED UNCLEAN. HERE GOD INDICATES IN THIS VISION THAT WHEN HE MAKES A THIN CLEAN, IT IS CLEAN INDEED. FORTHERMORE, WHEN A PERSON IS CLEANSED BY GOD, HE IS CLEAN INDEED VS 17 WHEN IN DOUBT ASK GOD. GOD PRESENTED THE VISION THREE TIMES (FOR CLEARITY. THIS WAS VERY SIGNIFICANT) AND WHILE PETER WAS STILL THINKING OR DOUBTING THE MEN WHICH WERE SENT FROM CORNELIUS ARRIVED. VS 19 WHILE PETER THOUGHT ON THE VISON, THE SPIRIT SAID UNTO HIM, BEHOLD, THREE MEN SEEK THREE ARISE THEREFORE AND GET THEE DOWN, AND GO WITH THEM, NOT DOUBTING: FOR I HAVE SENT THEM . GOD RESPONDED TO THE THOUGHTS OF HIS HEART. GOD RESPONDS TO THE TOUGHTS OF OUR HEART. THIS IS WHY IT IS IMPORTANT THAT WE HAVE JESUS IN OUR HEART. GOD DIRECTS AND ARRANGES THE AFFAIRS OF HIS CHILDREN. VS 22 THE MEN’S ACCOUNT. VS 23 HE TOOK THE MEN IN AND LODGED THEM AND WENT AWAY WITH THEM ON THE MORROW ---- WITH OTHERS. ORDINARILY JEWS AND GENTILES DO NOT ASSOCIATE WITH EACH OTHER. THIS EVENT BROUGHT THEM TOGETHER. THIS SHOWS THAT GOD IS GOD OF ALL.  THE BRETHREN WORKED TOGETHER VS 25 CORNELIUS MET PETER. HE HAD BEEN WAITING FOR THEM. HE CALLED TOGETHER HIS KINGSMEN AND NEAR FRIENDS. CORNELIUS FELL DOWN AT PETER’S FEET. AND WORSHIPED HIM. VS 26 BUT PETER TOOK HIM UP SAYING STAND UP, I MYSEF ALSO AM A MAN VS 28 HE EXPLAINED THAT HE CAME BECAUSE GOD HATH SHEWED HIM THAT HE SHOULD COT CALL ANY MAN COMMON OR UNCLEAN . VS 29 HE NOW ASKED WHY HE WAS SENT FOR. VS 30 – 31 NOTICE THAT CORNELIUS PRAYED AND FASTED YOUR PRAYER IS HEARD AND THINE ALMS ARE HAD IN REMEMBRANCE IN THE SIGHT OF GOD. VS 33 THEY WERE EAGER TO HEAR WHAT GOD HAD TO SAY. CORNELIUS EAGERLY AWAITED THE ARRIVAL OF PETER. HE RECEIEVED HIM WITH JOY AND LISTENED TO HIM ATTENTIVELY AND ACCEPTED THE GOSPEL WHOLE HEAREDLY AND GOD SAVED HIM AND HIS HOUSE HOLD AND FILLED THE WITH THE HOLY GHOST. YOU NEED TO BE EAGER TO HEAR GOD OR FROM GOD. READ YOUR BIBLE AND PRAY. PETER MINISTERED UNTO THEM. THEY REPENTED AND RECEIVED THE HOLY SPIRIT. VS 38 JESUS CHRIST WENT ABOUT DOING GOOD VS 42 JESUS CHRIST IS THE JUDGE OF THE QUICK AND DEAD. VS 43 TO HIM GIVE ALL THE PROPHETS WITNESS, THAT THROUGH HIS NAME WHOSOEVER BELIEVETH IN HIM SHALL RECEIVE REMISSION OF SINS. VS 44 WHILE PETER YET SPAKE THESE WORDS, THE HOLY GHOST FELL ON ALL THEM WHICH HEARD THE WORD VS 45 THEY OF THE CIRCUMSITION WHICH BELIEVED WERE ASTONISHED, BECAUSE THE GENTILES RECEIVED THE HOLY SPIRIT VS 48 THEY WERE BAPTIZED. THE STORY OF PETER AND HEROD

TRANSDUCERS IN ELECTRICAL POWER SYSTEMS ENGINEERING PROTECTION

TRANSDUCERS CONVERT HIGH VOLTAGES AND CURRENT TO LOWER VALUES FOR THE FOLLOWING REASONS 1) THE LOWER LEVEL INPUT TO THE RELAYS ENSURE THAT THE PHYSICAL HARDWARE USED TO CONSTRUCT THE RELAYS WILL BE QUITE SMALL AND THUS LESS EXPENSIVE. 2) THE PERSONNEL WHO WORK ON THE RELAYS WILL BE WORKING IN A SAFE ENVIRONMENT IN PRINCIPLE, THE TRANSDUCERS ARE SAME AS THE POWER TRANSFORMERS; PUT TO SPECIFIC USE. The current transformer is expected to produce a current in the secondary winding which duplicates the primary current waveform as faithfully as possible. THE AMOUNT OF POWER DELIVERED BY THESE TRANSFORMERS IS RATHER MODEST SINCE THE LOAD ON THEM IS EITHER RELAY AND METER AND USED ONLY WHEN NEEDED. THIS LOAD ON CT AND VT IS REFERRED TO AS THEIR BURDEN. BURDEN : THE IMPEDANCE CONNECTED TO THE TRANSFORMER SECONDARY WINDING. IT MAY ALSO BE REFERRED TO AS THE VOLTAMPERE DELIVERED TO THE LOAD. IE. IT MAY ALSO REFER TO THE VOLTAMPERE DELIVERED TO THE LOAD. EG. A TRANSFO RMER DELIVERING 5 AMPERES TO A RESISTIVE BURDEN OF 0.1 OHM CAN BE SAID TO HAVE A BURDEN OF 2.5VA VOLTAMPERES AT 5A, 5AMPERES. CT CURRENT TRANSFORMER CURRENT TRANSFORMERS HAVE RATIO ERRORS WHICH CAN AND ARE CALCULATED IN SOME CASES AND IN OTHER CASES HAVE TO BE MEASURED. IF IMPEDANCE BURDEN IS LARGE, THIS ERROR CAN BE HIGH. IF THE CT IS PROPERLY SELECTED WITH RESPECT TO THE BURDEN, THIS ERROR CAN BE MINIMIZED. CT BUILT WITHIN THE BUSHING THROUGH WHICH A TERMINAL OF THE POWER EQUIPMENT IS BROUGHT OUT……………ARE ALSO AVAILABLE HENCE CALLED BUSHING CT’S EQUIPMENT ENCLOSED IN GROUNDED TANKS FILLED WITH OIL INSULATING MEDIUM…….. ARE ALSO AVAILABLE THIS TYPE IS AVAILABLE IN DEAD - TANK SYSTEMS. EHV (- SWITCHING STATIONS) HERE LIVE – TANK CB ARE IN USE, FREE STANDING CURRENT TRANSFORMERS CT CURRENT RATING STANDARDISED AT 5A SECONDRIES. SECOND STANDARD 1A IN EUROPE FOR SHORT PERIODS, YOU CAN HAVE 10-20 TIMES THAT DURING SHORT CIRCUIT IN SECONDARY. CT RATIOS RANGE FROM 50: 5 - 1200: 5 CURRENT RATIO CURRENT TRANSFORMER RATIOS CURRENT TRANSFORMER RATIOS A:A 50A:5A 100A:5A 150A:5A 200A:5A 250A:5A 300A:5A 400A:5A 450A:5A 500A:5A 550A:5A 600A:5A 650A:5A 700A:5A 750A:5A 800A:5A 850A:5A 900A:5A 950A:5A 1000A:5A 1050A:5A 1100A:5A 1150A:5A 1200A:5A BURDEN BECAUSE IF FOR EXAMPLE 5 AMPERES IS DELIVERED BY A TRANSFORMER TO A RESISTIVE BURDEN OF 0.1OhM(Ω) THE TRANSFORMER MAY ALSO BE SAID TO HAVE A BURDEN OF 2.5 VOLTSAMPERES AT 5 AMPERES. THIS IS BECAUSE GIVEN V=IR V = .5V FOR I = 5A AND R =0.1Ω(Ohms) HENCE VI = .5X5 = 2.5VA VOLTAGE TRANSFORMER TWO TYPES EXIST 1) FOR LOW - VOLTAGE APPLICATION SYSTEM VOLTAGES 12 Kv or LOWER PRIMARY WINDING AT SYSTEM VOLTAGE AND SECONDARY WINDING AT 67V (THIS REPRESENTS SYSTEM LINE TO NEUTRAL VOLTAGE ) 67V*√3 = 116V REPRESENTING THE SYSTEM LINE TO LINE VOLTAGE ) ARE AN INDUSTRIAL STANDARD. THIS IS SIMILAR TO A MULTIWINDING POWER TRANSFORMER AND BECOMES EXPENSIVE AT HIGHER SYSTEM VOLTAGES. AT HV AND EHV LEVELS, A CAPACITANCE POTENTIAL – DIVIDER CIRCUIT IS USED. C1 AND C2 ARE ADJUSTED SO THAT A VOLTAGE OF A FEW kV IS OBTAINED ACROSS C2 WHEN TERMINAL A IS AT SYSTEM POTENTIAL. IN SUCH A COUPLING CAPACITOR VOLTAGE TRANSFORMER (CVT) THE TAPPED VOLTAGE IS FURTHER REDUCED TO RELAYING VOLTAGE LEVEL BY A TRANSFORMER. CIRCUIT DIAGRAM OF A CAPACITOR – COUPLED VOLTAGE TRANSFORMER CVT WITH ITS TUNING INDUCTANCE L. IN SUCH A COUPLING CAPACITOR VOLTAGE TRANSFORMER (CCVT) (CVT) THE TAPPED VOLTAGE IS FURTHER REDUCED TO RELAYING VOLTAGE LEVEL BY A TRANSFORMER. THE VOLTAGE AT POINT A CAN BE CONSIDERED TO BE THAT OF AN INFINITE BUS SO FAR AS THE CONNECTED CAPACITORS ARE CONCERNED.

RETARDED POTENTIALS CONTINUED

RETARDED POTENTIALS CONTINUED IF ρ IS CHANGING WIH TIME, CONSIDER THE FIGURE BELOW P HAVE POSITION VECTOR r AND Q HAS POSITION VECTOR r’ IF CHARGE DISTRIBUTION NEAR Q CHANGES WITH TIME, THE INFORMATION THAT IT HAS CHANGED CAN ONLY BE APPRECIATED AT POINT P AT TIME |r-r’|/C AFTER THE CHANGE. THIS IS THE TIME IT TAKES THE ELECTROMAGNETIC RADIATION TO TRAVEL THE DISTANCE |r –r’| HENCE IT IS PLAUSIBLE THAT AT A TIME t THE CONTRIBUTION TO THE POTENTIAL Φ(r,t) AT P FROM THE CHARGE WITHIN THE VOLUME ELEMENT 𝜕τ’ AT Q DEPENDS NOT ON WHAT THE CHARGE IS AT TIME t BUT ON WHAT IT WAS AT TIME t-|r-r’|/C THIS IS TRUE FOR ALL THE VOLUME ELEMENTS WITHIN THE VOLUME V. NOTE THAT C IS THE SPEED OF LIGHT WHICH IS ALSO THE SPEED OF PROPAGATION OF ELECTROMAGNETIC WAVES AND FIELDS. NB: THE TIME LAPSE |r-r’|/C DEPENDS ON THE POSITION VECTOR r’ AND HENCE VARIES OVER THE VOLUME V Φ(r,t) = (1/4πε0)∫v((ρ(r’,(t-|r-r’|)/C)/(|r-r’|)).dτ’) (&&&&&) Similarly THE SOLUTION TO THE EQUATION(&&&) GIVES POTENTIAL A THIS IS GIVEN BY A(r,t) = (𝝻0/4π) Φ(r,t)∫v((j(r’,(t-(|r-r’|)/C)/(|r-r’|)).dτ’) (&&&&&&) THE SOLUTION TO EQUATION (&&) HENCE OBTAINED BY INTEGRATING THE CONTRIBUTIONS OVER THE VOLUME V

RETARDED POTENTIALS

RETARDED POTENTIALS RETARDED POTENTIALS ARE SO CALLED BECAUSE THE COTRIBUTION OF EACH ELEMENT OF CHARGE AND CURRENT IS DELAYED BY THE TIME TAKEN FOR LIGHT TO TRAVEL TO THE POINT WHERE THE POTENTIAL IS BEING CALCULATED. INFORMATION ABOUT THE PRESENT VALUE OF CHARGE AND CURRENT PROPAGATESOUTWARDS AT A SPEED C. IF THE CHARGE DISTRIBUTION NEAR Q CHANGES WITH TIME, THE INFORMATION THAT IT HAS CHANGED CAN ONLY BE APPRECIATED AT THE POINT P A TIME |r-r`|/C AFTER THE CHANGE. THIS IS THE TIME IT TAKES ELECTROMAGNETIC RADIATION TO TRAVEL THE DISTANCE |r-r`| PROCEDURE FOR SOLVING PROBLEMS OF RETARDED POTENTIALS WE START BY USING THE LORENTZ TRANSFORMATION TO FIND THE POTENTIALS GENERATED BY A SMALL CHARGE WHEN IT IS VIEWED FROM A MOVING FRAME OF REFERENCE. THEN THE POTENTIALS CAUSED BY ANY DISTRIBUTION OF CHARGE AND CURRENT CAN BE FOUND BY SUPERPOSITION. IF WE WISH TO RELATE THE FIELDS TO THE CHANGING CHARGE AND CURRENT DISTRIBUTION WHICH PRODUCE THEM, IT IS EASIER TO WORK WITH THE POTENTIALS; THAN WITH THE FIELDS DIRECTLY. WE WILL OUTLINE THE STEPS TAKEN TO OBTAIN THE POTENTIALS IN TERMS OF GIVEN CHARGE AND CURRENT DISTRIBUTIONS. ONCE THE POTENTIALS HAVE BEEN DETERMINED THE FIELDS CAN BE OBTAINED FROM THE RELATIONSHIPS BELOW B = CURL A (*) B≡MAGNETIC FIELD B A≡MAGNETIC VECTOR POTENTIAL H≡MAGNETIC FIELD INTENSITY(STRENGTH) E =-(𝜕A/𝜕t) – gradΦ (**) Φ ≡ ELECTROSTATIC POTENTIAL (IF THE FIELDS ARE INDEPENDENT OF TIME) OTHERWISE IF VARYING WITH TIME JUST ELECTRIC POTENTIAL E ≡ ELECTRIC FIELD D ≡ ELECTRIC DISPLACEMENT FIRST WE DERIVE DIFFERENTIAL EQUATIONS OBEYED BY THE POTENTIALS A AND Φ SEPARATELY. WE ONLY CONSIDER CHANGING CHARGE AND CURRENT DISTRIBUTION IN FREE SPACE (FREE SPACE OR AIR.) MAXWELL’S EQUATIONS BECOME div E = ρ/ε0 (***) divB = 0 Curl E = -𝜕B/𝜕t (1/𝜇0)Curl B = j + ε0𝜕E/𝜕t (@) where: D = εε0E H=B/𝜇𝜇0 SUBSTITUTE FOR E IN (***) USING (**) TO GET -∇2Φ – (𝜕/𝜕t)(divA) = ρ/ε0 (****) NB. IF f(x,y,z) IS A TWICE DIFFERENTIABLE SCALAR FUNCTION, THEN grad f =(𝜕f/𝜕x)i+(𝜕f/𝜕y)j+(𝜕f/𝜕z)k THE div V= (𝜕V1/𝜕x)+(𝜕V2/𝜕y)+(𝜕V3/𝜕z) = ∇.V = (𝜕/𝜕xi+𝜕/𝜕yj+𝜕/𝜕zk).(V1i+V2j+V3k) = div(grad f) = (𝜕2f/𝜕x2)+(𝜕2f/𝜕y2)+(𝜕2f/𝜕z2) div(grad f ) =∇2.f THIS IS THE LAPLACIAN OF f THE POTENTIALS A AND Φ ARE NOT UNIQUELY SPECIFIED BY EQUATIONS (*) AND (**) WE CAN ADD TO THE VECTOR A ANY FUNCTION WHOSE CURL IS ZERO AND THE SAME MAGNETIC FIELD RESULTS. WE CAN ADD TO THE POTENTIAL Φ ANY FUNCTION WHOSE GRADIENT IS ZERO AND THE SAME ELECTRIC FIELD RESULTS. WE ARE AT LIBERTY TO IMPOSE ANY CONDITION ON THE FUNCTION A AND Φ THAT DOES NOT CONTRADICT MAXWELL’S EQUATIONS. IN THIS DISCUSSION OF STEADY MAGNETIC FIELD WE ADDED THE CONDITION div A = 0 WITH TIME – DEPENDENT FIELDS, IT IS CONVINIENT TO GENERALIZE THIS TO div A= - ε0𝝻0𝜕Φ/𝜕t (&) THE RESTRICTION ON THE POTENTIALS IMPOSED BY EQUATION & ABOVE IS KNOWN AS THE LORENTZ CONDITION. IT INTRODUCES A SYMMETRY INTO THE EQUATIONS FOR THE POTENTIAL. IT ALSO ENABLES ELECTROMAGNETISM TO BE BROUGHT INTO LINE WITH THE SPECIAL THEORY OF RELATIVITY. SUBS (&) INTO (****) TO GET -∇2Φ + ε0𝝻0𝜕2Φ/𝜕t2 =ρ/ ε0 (&&) NOTICE THAT THIS EQUATION INVOLVES Φ ALONE. Ie THE POTENTIAL Φ IN THE AREAS OF SPACE WHERE ρ IE CHARGE DENSITY IS ZERO, THE POT5ENTIAL Φ OBEYS THE SAME WAVE EQUATION AS THE FIELDS E AND B. THE EQUATION FOR THE VECTOR POTENTIAL A CAN BE OBTAINED BY SUBSTITUTING (*), AND (**)IN (@). THEN USING LORENTZ CONDITION LEADS TO AN EQUATION SIMILAR TO EQUATION (&&) ABOVE. -∇2A + ε0𝝻0𝜕2A/𝜕t2 =𝝻0j (&&&) THESE ARE THE DIFFERENTIAL EQUATIONS FOR THE POTENTIALS. A SOLUTION OF THESE EQUATIONS GIVE RISE TO THE POTENTIALS A AND Φ IN TERMS OF THE CHARGE AND CURRENT DISTRIBUTIONS WE WILL SOLVE THIS PROBLEM BY INFERENCE IE NOT DIRECTLY BUT USE THE ANOLOGY WITH THE SOLUTION OF TIME INDEPENDENT PROBLMS DISCUSSED IN ELECTROSTATICS AND MAGNETOSTATCS. IN ELECROSTATICS, WE SOLVE THE PROBLEM -∇2Φ =ρ/ ε0 NB: THE FIELDS ARE STATIC HENCE THE DIFFERENTIAL OF THE FIELD IS ZERO. IE. THAT COMPONENT REMOVED FROM THE TIME VARYING POTENTIAL DIFFERENTIAL EQUATION. (ε0𝝻0𝜕2Φ/𝜕t2 ≡ FOR TIME VARYING FIELDS) THE SOLUTION IS Φ(r) = (1/4πε0)∫v((ρ(r’)/(|r-r’|))dτ’) Where V: Volume occupied by the Charge distribution ρ This is the solution of the equation: -∇2Φ = ρ/ ε0

LET US FEAR GOD AND WORK RIGHTEOUSNESS

THE STORY OF PETER ACTS 10 AND ACTS 12 THE STORY OF CONELIUS ACTS 10:35 GOD IS NO RESPECTER OF PERSON BUT IN EVERY NATION EVERYONE WHO FEARS HIM AND DOES RIGHTEOUSNESS IS ACCEPTABLE UNTO HIM. GOD IS NO RESPECTER OF PERSONS BUT IN EVERY NATION HE THAT FEARETH HIM AND WORKETH RIGHTEOUSNESS, IS ACCEPTED WITH HIM. ACTS 10 VS 1 A CERTAIN MAN IN CEASAREA CALLED CORNELIUS A CENTURION OF THE BAND CALLED THE ITALIAN BAND. VS 2 A DEVOUT MAN AND ONE THAT FEARED GOD WITH ALL HIS HOUSE, WHICH GAVE MUCH ALMS TO THE PEOPLE, AND PRAYED TO GOD ALWAYS. THIS WAS A MAN JUST LIKE ANY OTHER MAN HE WAS A CENTURION. HE WAS A DEVOUT MAN AND HE FEARED GOD WITH ALL HIS HOUSE. HE ENSURED THAT HIS HOUSE FEARED GOD. PARENTS SHOULD ENSURE THAT THEY FEAR GOD WITH ALL THEIR HOUSE. HE GAVE MUCH ALMS TO THE PEOPLE AND PRAYED TO GOD ALWAYS. NOTICE THAT THIS MAN SPENT TIME IN PRAYER WITH GOD ALWAYS. HE ALSO GAVE MUCH ALMS TO THE PEOPLE. WHEN YOU SPEND TIME WITH GOD, IT IS EASIER TO DO GOOD TO MEN. GOD IS THE SOURCE OF ALL GOOD THINGS. IT IS IMPORTANT TO PRAY TO GOD ALWAYS. THE STORY OF PETER AND HEROD

JOY

JOY JOY IS A NOUN REJOICE IS A VERB WHEN YOU REJOICE, YOU HAVE JOY IN YOUR HEART WHEN YOU REJOICE YOU ARE JOYFUL. QUESTIONS: - WHAT BRINGS ABOUT JOY? - WHAT MAKES YOU TO REJOICE? LIKE MOST THINGS WE DO, WE NEED CAPACITY AND ABILITY TO REJOICE. NOTICE THAT IN THE BIBLE, WHEN PEOPLE SINCERELY HAVE AN ENCOUNTER WITH JESUS CHRISTFOR THE RIGHT REASONS AND WITH THE RIGHT MOTIVES AND THEY ACCEPT HIM(JESUS CHRIST) AND OBEY HIM (JESUS CHRIST) AND CARRY OUT HIS DIRECTIVES AND INSTRUCTIONS, MAKING HIM LORD AND SAVIOUR, THEY GO ABOUT REJOICING . WHEN THE REVERSE IS THE CASE, THEY GO AWAY SOROWING. JUST AS THE REACH MAN WHO WAS ASKED TO SELL WHAT HE HAD AND GIVE TO THE POOR AND FOLLOW JESUS CHRIST. MT.19:22, LK18:23 THIS SHOWS THAT CONTACT WITH JESUS CHRIST BRINGS JOY. JESUS CHRIST TAKES AWAY OUR SINS AND LEAVES US REJOICING EVERMORE. REPENTANCE BRINGS JOY FORGIVENESS BRINGS JOY THE JOY OF THE LORD IS OUR STRENGTH THE WORD OF THE LORD BRINGS JOY AN ENCOUNTER WITH GOD BRINGS JOY OBEDIENCE BRINGS JOY SALVATION BRINGS JOY. Jn 14:28 If you love me ye would rejoice. The sincere love of and for our Lord Jesus Christ will make you to rejoice. If you are not rejoicing, ask yourself why? Ask yourself about your sincere love for our lord Jesus Christ. Jesus Christ in you will bring joy to you. Let us believe in our lord Jesus Christ today for our salvation and He will keep us rejoicing for evermore and give us an everlasting joy.

PROTECTION

PROTECTION ZONE OF PROTECTION The idea of an area of responsibility of a protection system mentioned above has been formalized by assigning zones of protection to various protection systems. This concept of zones help to define the reliability requirements for different protection systems. Each breaker is included in two neighbouring zones of protection. The boundry of each zone defines a portion of the power system such that for a fault anywhere within that zone, the protection system responsible for that zone takes action to isolate everything within that zone from the rest of the system. The CB. Circuit Breaker help to define the boundries of the zones of protection. This is because at each point where connection is made b/w equipment inside the zone and the rest of the power system, a CB. Is or should be inserted because isolation under faulted condition is achieved through a CB. Neighbouring zones always overlap. This is important so that small parts of the system do not get left out without protection. The region of overlap is however made as small as possible to reduce very large disruptions to the system.