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# Elect Circuit Theo EEN 201

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This 28 page Class Notes was uploaded by Silas Goldner on Thursday September 17, 2015. The Class Notes belongs to EEN 201 at University of Miami taught by M. Scordilis in Fall. Since its upload, it has received 17 views. For similar materials see /class/205723/een-201-university-of-miami in ELECTRICAL AND COMPUTER ENGINEERING at University of Miami.

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Date Created: 09/17/15

CIRCUITS 1 V 3 v DEVELOP TOOLS FOR THE ANALYSIS AND DESIGN OF BASIC LINEAR ELECTRIC CIRCUITS A FEW WORDS ABOUT ANALYSIS USING MATHEMATICAL MODELS BASIC STRATEGY USED IN ANALYSIS Phy a1 device Interpretation of resu ls Solution procedure 0 De ne variables Write equations I Solve equations WHOJ EIHJ IO SNOIiVnOEI 39IVLLNEIHEHJICI 38 TIIV S39IEICIOW EIHL HEIJV39I SNOIJVnOEI DIVHEEI DquotV IO SWEIJSAS EINIOS OJ CIELLDEIdXEI 38 TIIV EMA JHVd LSHH EIHJ HOJ S39IEICIOIN 39IVDIJVWEIHJVW EIHJ EIA39IOS OJ S39IOOJ EIHJ EICIIAOHd SNOJVnOEI 39IVIJNEIEEIIIICI CI VEIEIEID39IV EIVEINI39I 19 SEISSV39IZ SDIJVWEIHJVIN EIHJ NOIiISOdHIldnS IO El39ldIDNIHd EIHL AJSIJVS AEIHL JVHL SNVEIW HDIHM EIVEINI39I 38 TIIV AEIHJ HV InDIJHVd NI 39SEIIJHEIdOHd 39IVDIJVWEIHJVW EDIN ElVH ClEldO39IEIEICI 38 TIIV JVHL S39IEICIOIN EIHL SJJFDHD DIHJDEI IEI HOJ STEICIOW quotIVDIJVWEIHJVW dOquotElEIC OL SEanINHDELL DISVEI EHL SEIHDVEIJ asunoa SIHJ NOLVnJS NEIAID V NI HAVHEIEI TllV ilnDHID EIHL VOH EINIINHEIJLICI OJ quotIEICIOIN EIHL ElOS OJ VOH NHVEH 39 39IEICIOIN 39IVDJVNEIJVN V 39 ilnDHD EIHJ JNEISEIHdEIH JVHJ SNOIJVnOEI quotIVDIJVWEIHJVW IO JES V dOquotElEIC SISA39IVNV 39IVCIJVNEIHLVIN r ELECTRIC CIRCUIT IS AN INTERCONNECTION OF ELECTRICAL COMPONENTS 2 TERMINALS COM PONENT L J characterized by the current through it and the voltage difference between terminals NODE NODE L R R TYPICAL LINEAR 2 V0 CIRCUIT VS C LOW DISTORTION POWER AMPLIFIER The concept of node is extremely important We must learn to identify a node in any shape or form DU 7 g v T 2 JP 7 7439 I GEAUX gt BASIC CONCEPTS LEARNING GOALS I System of Units The SI standard system prefixes Basic Quantities Charge current voltage power and energy Circuit Elements Active and Passive The NIST Reference on httpphysrcsnlstgovcuundexhtm Constants Units and Uncertainty I l nternational System of Units SI SI base units The SI is founded on seven 5 base units for seven base quantities assumed to be mutually independent as given in Table 1 Table 1 SI base units SI base unit Base quantity Name Symbol length meter In mass kilogram kg time second s electric current ampere A thermodynamic temperature kelVin K amount of substance mole mol luminous intensity candela cd For detailed information on the SI base units see Definitions of the 5 base units and their Historical come n Definitions of the SI base units unit of ength meter The meter is the length of the path travelled by light in vacuum during a time interval of 1299 792 458 ofa second Unit of mass kilogram The kilogram is the unit of mass it is equal to the mass ofthe international prototype of the kilogram Unit of time second The second is the duration of 9192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels ofthe ground state of the cesium 133 atom Unit of ampere The ampere is that constant current dad current which if maintained in two straight parallel conductors of infinite length of negligible circular cross section and placed 1 meter apart in vacuum would produce between these conductors a force equal to 2 x 10397 newton per meter of length Unit of kelvin The kelvin unit of thermodynamic thermodynamic temperature is the fraction 127316 of temperature the thermodynamic temperature of the triple point of water Unit of mole 1The mole is the amount of substance amount of ofa system which contains as many substance elementary entities as there are atoms in 0012 kilogram of carbon 12 its symbol is imol39u The 20 SI pre xes used to form decimal multiples and submultiples of SI units are given in Table 5 Table 5 SI prefixes Factor Name Symbol Factor Name Symbol 1024 yotta Y 10391 deci d 1021 zetta Z 10392 centi c 1018 exa E 10 3 milli m 1015 peta P 10396 micro u 1012 tera T 10 9 nano n 109 giga G 103912 pico p 106 mega M 103915 femto f 103 kilo k 103918 atto a 102 hecto h 103921 zepto z 101 deka da 103924 yocto y SI DERIVED BASIC ELECTRICAL UNITS power radiant ux electric charge quantity of electricity electric potential difference electromotive force capacitance electric resistance electric conductance magnetic ux magnetic ux density inductance watt coulomb volt farad 011m Siemens weber tesla henIy W C 2 Wb J S mzkgs393 sA WA mZ kgs393 A391 CV m39Zlltg39139s4A2 VA mz39kgs393A392 AN m2kg 153A2 v5 m2kgS2A1 Wbm2 kgS39ZA391 WbA mzkg39s z39A392 Charge Current Voltage and Power ONE AMPERE OF CURRENT CARRIES ONE COULOMB OF CHARGE EVERY SECOND A Cs 1 COULOMB 628gtlt1018 e e IS THE CHARGE OF ONE ELECTRON VOLT IS A MEASURE OF ENERGY PER CHARGE TWO POINTS HAVE A VOLTAGE DIFFERENCE OF ONE VOLT IF ONE COULOMB OF CHARGE GAINS ONE JOULE OF ENERGY WHEN IT IS MOVED FROM ONE POINT TO THE OTHER OHM IS A MEASURE OF THE RESISTANCE TO THE FLOW OF CHARGE THERE IS ONE OHM OF RESISTENCE IF IT IS REQUIRED ONE VOLT OF ELECTROMOTIVE FORCE TO DRIVE THROUGH ONE AMPERE OF CURRENT V 97 A IT IS REQUIRED ONE WA39I39I39 OF POWER TO DRIVE ONE AMPER OF CURRENT AGAINST AN ELECTROMOTIVE DIFFERENCE OF ONE VOLTS PVxA m Current in amperes A CURRENT AND VOLTAGE RANGES Lightning holt Large industrial motor current Typical household appliance current Causes ventricular fibrillation in humans Human threshold of sensation integrated Circuit memory cell current Synaptic current brain cell Voltage in Volts V Lightning bolt High voltage transmission lines Vollage on a TV picture tube Large industrial motors AC outlet plug in US households Car batte Voltage on integrated circuits Flashlight battery Voltage across human chest produced by the heart EKG Voltage between two points on human scalp Antenna of a radio receiver Strictly speaking current is a basic quantity and charge is derived However physically the electric current is created by a movement of charged particles An electric circuit is essentially a pipeline that facilitates the transfer of charge from one point to another The time rate of change of charge constitutes an electric current Mathematically the relationship is expressed as dt or qt I ix ix ae Although we know that current ow in metallic conductors results from electron Ino lion the conventional current flow which is universallv adoptedi represents the move ment of positive charges What is the meaning of a negative value for 11 9 e PROBLEM SOLVING TIP IF THE CHARGE IS GIVEN DETERMINE THE CURRENT BY DIFFERENTIATION IF THE CURRENT IS KNOWN DETERMINE THE CHARGE BY INTEGRATIO A PHYSICAL ANALOGY THAT HELPS VISUALIZE ELECTRIC m CURRENTS IS THAT or WATER FLOW CHARGES ARE VISUALIZED As WATER PARTICLES m quot I I JIEI39JHDEI MO39H lHDlHl 39l MO39H NOILDHHIG EDNEIEIEHEIEI SHDHVHD EIAIJJSOd SHDHVHD EIAIJJSOd EIHL NVHJ NOILDHHIG ElllSOddO EIHL NI MO39H VS quot 11 Vg quot 11 SEILVDICINI lNEIEIEIrD EIHL HOd Eln39lVA EIAILVDEIN v V t I 1 VS 11 1 1 VS 1 NOILDHHIG EDNEIEIEHEIEI I mmD EIHJ MOHEIV EIHJ IO q A 1 NOIJDEIEIICI EIHJ NI MO39H VS I 39 VS I SEILVDICINI lNHHHnD EIHJ w I HOI EIn39IVA EIAIJJSOd V V C I NOIJDEIEIICI EIDNEIEIEHEIEI EIHJ SEIDEIVHD EIAIJJSOd HOI MO39H IO NOILDHHIG EIHJ EILVDICINI EIM CINV 39SHDHVHD EIAIJJSOd IO MO39H VS 4 q V9 1 SI iNHHH D JVHL SI DNmaaNIDNa 1V3HLDEI1EI 0 9 NI NOILNEIANOD aamaaav ATIVSEIEIAINn ElHJ EIINVN lNHHHnD EIHJ HOI SEIDICINIElnS SV INEIHJ EILVDICINI NVD EINO CIEI39IEIEIV39I EIHV EICION quotWWI HEM CINV 39IVLLINI EIHJ II NOIlVlON XEIGNI El39lEanG ElHJ 39SEI39IDILEIVd CIEIDEIVHD IO JNEINEION IO NOILDHHIG EIHJ EILVDICINI OJ AHVSSEDEIN A39IEIln39IOSEIV SI J SlNEIHHnI HOI NOIlNEIANOI This example illustrates the various ways in which the current notation can be used CONVENTIONS FOR VOLTAGES ONE DEFINITION FOR VOLT TWO POINTS HAVE A VOLTAGE DIFFERENTIAL OF ONE VOLT IF ONE COULOMB OF CHARGE GAINS OR LOSES ONE JOULE OF ENERGY WHEN IT MOVES FROM ONE POINT TO THE OTHER IF THE CHARGE GAINS ENERGY MOVING FROM a T0 b THEN b HAS HIGHER VOLTAGE THAN a IF IT LOSES ENERGY THEN b HAS LOWER VOLTAGE a THAN a 1C DIMENSIONALLY VOLT IS A DERIVED UNIT VOLT JOULE Nom COULOMB Aos VOLTAGE IS ALWAYS MEASURED IN A RELATIVE FORM AS THE VOLTAGE DIFFERENCE BETWEEN TWO POINTS IT IS ESSENTIAL THAT OUR NOTATION ALLOWS US TO DETERMINE WHICH POINT HAS THE HIGHER VOLTAGE I W A c n f7 I 1 I Iquot I l V c 1quot I u I I i quot 0 1 B t THE AND SIGNS DEFINE THE REFERENCE POLARITY IF THE NUMBER V IS POSITIVE POINT A HAS V VOLTS MORE THAN POINT B IF THE NUMBER V IS NEGATIVE POINT A HAS IVI LESS THAN POINT B Vl2V H ur n1Hf39j POINT A HAS 2V MORE THAN POINT B POINT A HAS 5V LESS THAN POINT B THE TWOINDEX NOTATION FOR VOLTAGES INSTEAD OF SHOWING THE REFERENCE POLARITY WE ENERGY VOLTAGE IS A MEASURE OF ENERGY PER UNIT CHARGE CHARGES MOVING BETWEEN POINTS WITH DIFFERENT VOLTAGE ABSORB OR RELEASE ENERGY THEY MAY TRANSFER ENERGY FROM ONE POINT TO ANOTHER BASIC FLASHLIGHI Converts energy stored in battery to thermal energy in lamp filament which turns incandescent and glows EQUIVALENT CIRCUIT The battery supplies energy to charges Lamp absorbs energy from charges Ky The net effect is an energy transfer Charges gain energy here gt Charges supply Energy here I W ENERGY VOLTAGE IS A MEASURE OF ENERGY PER UNIT CHARGE CHARGES MOVING BETWEEN POINTS WITH DIFFERENT IIIOLTAGE ABSORB OR RELEASE ENERGY WHAT ENERGY IS REQUIRED TO MOVE 120C FROM POINT 5 TO POINT A IN THE CIRCUIT THE CHARGES MOVE TO A POINT WITH HIGHER VOLTAGE THEY GAINED OR ABSORBED ENERGY THE CIRCUIT SUPPLIED ENERGY TO THE CHARGES VgWVQ24OJ THE VOLTAGE DIFFERENCE IS 5V Five joules of be from Quint B 10 ppim A in l 5 Find the voltage betwsen points A and B WHICH POINT HAS THE HIGHER VOLTAGE VAR SV EXAMPLE A CAMCODER BATTERY PLATE CLAIMS THAT THE UNIT STORES 2700mAHr AT 72V WHAT IS THE TOTAL CHARGE AND ENERGY STORED CHARGE THE NOTATION 2700mAHr INDICATES THAT THE UNIT CAN DELIVER 2700mA FOR ONE FULL HOUR Q 2700 gtlt103C 3600i gtlt1Hr S Hr 2972gtlt103C TOTAL ENERGY STORED THE CHARGES ARE MOVED THROUGH A 72V VOLTAGE DIFFERENTIAL J 3 W QC gtlt VL 972 X 10 X 72J 6998gtlt104J ENERGY AND POWER I A A I2A 2Cs PASS THROUGH THE ELEMENT B I2A EACH COULOMB OF CHARGE LOSES 3 OR SUPPLIES 3 OF ENERGY TO THE ELEMENT THE ELEMENT RECEIVES ENERGY AT A RATE OF 6ls THE ELECTRIC POWER RECEIVED BY THE ELEMENT IS 6W t2 IN GENERAL wt27t1 IPxdx P 2 VI t1 HOW DO WE RECOGNIZE IF AN ELEMENT SUPPLIES OR RECEIVES POWER I PASSIVE SIGN CONVENTION POWER RECEIVED Is POSITIVE WHILE POWER THIS IS THE REFERENCE FOR POLARITY SUPPLIED IS CONSIDERED NEGATIVE a IF VOLTAGE AND CURRENT lab v ARE BOTH POSITIVE THE 1 r gt T b CHARGES MOVE FROM IF THE REFERENCE DIRECTION FOR CURRENT lab HIGH TO Low VOLTAGE 395 GIVEN AND THE COMPONENT RECEIVES ENERGY IT IS A PASSIVE ELEMENT EXAMPLE A CONSEQUENCE OF THIS CONVENTION IS THAT V A THE REFERENCE DIRECTIONS FOR CURRENT AND 1 V 2 VOLTAGE ARE NOT INDEPENDENT IF WE ASSUME PASSIVE ELEMENTS I I lab b Vab 1 GIVEN THE REFERENCE POLARITY A THE ELEMENT RECEIVES 20W OF POWER 7 b WHAT IS THE CURRENT 4 SELECT REFERENCE DIRECTION BASED ON a I PASSIVE SIGN CONVENTION I b Vablab 10VIab REFERENCE DIRECTION FOR CURRENT ab UNDERSTANDING PASSIVE SIGN CONVENTION We must examine the voltage across the component and the current through it I I A A PS1 2 VABIAB V I PS2 2 VA B IA B B B CurrentA A39 S1 82 ON 51 ON 52 OSItIve SItIve IIes receives AB gt 0 AB lt 0 VAR gt 0 AB gt 0 os rece s 39tive receives ON 52 SI VABlt01ABgt0 3 lies m Good battery CHARGES RECEIVE ENERGY CHARGES LOSE ENERGY THIS BATTERY SUPPLIES ENERGY THIS BATTERY RECEIVES THE ENERGY WHAT WOULD HAPPEN IF THE CONNECTIONS ARE REVERSED IN ONE OF THE BATTERIES CIRCUIT ELEMENTS PASSIVE ELEMENTS VOLTAGE DEPEN DENT SOURCES AGE 3 gttgva UNITS FOR ngrj D i0 l I39l CURRENT b i DEPENDENT SOURCES lt 1 a b c D 551 EXERCISES WITH DEPENDENT SOURCES IS 1 mA o FIND V0 V0 40V FIND 10 10 SOmA DETERMINE THE POWER SUPPLIED BY THE DEPENDENT SOURCES 02A V P 40V2AD 80W P 10V4gtlt 4A160W TAKE VOLTAGE POLARITY REFERENCE TAKE CURRENT REFERENCE DIRECI39ION m POWER ABSORBED 0R SUPPIJED BY EACH USE POWER BALANCE T0 COMPUTE lo I ELEMENT I P1 12V4A 48W P ex 2 12 w P2 24V2A 48W P1 6M 6W P3 28V2A 56W 102 12x79 403w PDS 1199M 4V72A 78W P 103 30 W PW 36V74A 7144W Pov 4W8 32 W Pm 81301 1611 176W NOTICE THE POWER BALANCE POWER BALANCE 1261071087307321760 101A

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