Experiment 3: Ian Camus #1, Shizhao Chen *2, Marvilette Jequinto #3, Jerome opena #! S"hool o Me"hani"al an$ Manua"turin% En%ineerin%, Mapua Institute o &e"hnolo%' Muralla Street, Intramuros, Manila, (hilippines 1
[email protected] 2
[email protected] 3
[email protected] 4
[email protected]
Abstract – Experiment 3 is about the analysis of resistive networks using Kirchhoff’s law. The same circuit from experiment was use! in this experiment to !etermine the voltages an! currents across each circuit elements. The resistances were selecte!" an! then the value of the voltages an! currents were measure! using the #$$ for the voltage an! ammeter for the current. The calculate! values were !etermine! using the Kirchhoff’s %urrent law an! Kirchhoff’s &oltage 'aw. A simulation using Tina (ro was also !one. The results from the measure!" calculate! an! simulate! values were close to each other.
I) I&+-.C&I /ustav 0ir"hho is a /erman mathemati"ian ho as orn in 0ni%ser%, the ormer "apital o (russia) 415It as hile he as stu$'in% ith eumann ho ' the 'ear 16!7 ha$ pulishe$ his to ma8or papers on ele"tri"al ele"tri"al "on$u"tion, that 0ir"hho ma$e his irst outstan$in% resear"h "ontriution hi"h relate$ to ele"tri"al "urrents) &he sai$ resear"h is the 0ir"hho9s 0ir"hho9s las, hi"h he announ"e$ in 16!7, alloe$ "al"ulation o "urrents, volta%es an$ resistan"es in ele"tri"al "ir"uits ith multiple loops, exten$in% the or o hm) 0ir"hho "onsi$ere$ an ele"tri"al netor "onsistin% o "ir"uits 8oine$ at no$es o the netor an$ %ave las hi"h re$u"e the "al"ulation o the "urrents in ea"h loop to the solution o al%erai" equations) &he irst la states that the sum o the "urrents into a %iven no$e equals the sum o the "urrents out o that no$e) &he se"on$ l a states that the sum o ele"tromotive or"es in a loop in the netor equals the sum o potential $rops, or volta%es a"ross ea"h o the resistan"es, in the loop) 0ir"hho9s 0ir"hho9s Current a states that the summation o all "urrent ithin a %iven no$e is equivalent to zero, or in other or$s, the summation o all "urrent enterin% the no$e or 8un"tion is equivalent to the summation summation o all "urrent "urrent leavin% the no$e or 8un"tion) 425; no$e or a 8un"tion is a point on the "ir"uit at hi"h to or more elements have a "ommon "onne"tion) 0ir"hho9s Current a, is the la o "onservation o "har%e in ele"tri" "ir"uits sin"e Current is "har%e <"oulom= per se"on$)
0ir"hho9s irst la: 0ir"hho9s Current a <0C= >???????@A or >? ????????@ >? ??????? &he se"on$ la is the 0ir"hho9s Bolta%e a herein the summation o all volta%espotential aroun$ a %iven "lose$ path or loop is equivalent to zero) In other or$s, the summation o all volta%epotential rise is equivalent to the summation o all volta%epotential $rop) ; path is a set o no$e an$ elements passe$ throu%h i no no$e as as en"ountere$ more more than on"e hile a "lose$ path or loop is a in$ o path herein the no$e here 'ou starte$ is also the no$e here 'ou ill en$) &he $ire"tion o path "oul$ either e "lo"ise or "ounter "lo"ise) &he si%n "onvention or ea"h volta%e $epen$s on here the path or loop entere$ or let) &he $ire"tion use$ must e "onsistent throu%h all the loops) 0ir"hho9s 0ir"hho9s Bolta%e a is re"o%nize$ as the appli"ation o the a o Conservation o Ener%' sin"e Bolta%e is Joule per "oulom) 0ir"hho9s se"on$ la: 0ir"hho9s Bolta%e a <0B= >????????@A or >? ????@ >? ????? II) M;&E+I;S ;- ME&D&he materials use$ use$ in the experiment are are the olloin%: Cir"uit 1 trainer it
Gi%ure 1: &he "ir"uit use$ in the experiment
;pplie$ the hm9s la, B @ I+, an$ usin% the 0ir"hho9s Bolta%e a to "omplete the $ata in &ale 3)1)
Conne"t the "ir"uit shon in the Gi%ure 1 ' usin% the poer suppl' an$ the trainer it) Che" i it is properl' "onne"te$ eore turn on the poer suppl');n$ then, the volta%e supplie$ in the "ir"uit must e equal to 2AB)
Gi%ure !: -ia%ram ma$e ' usin% the &ina (ro pro%ram Gi%ure 2: Give resistors ere use$ in the experiment) Measure the resistan"e values o ive resistors ' usin% a multiFmeter an$ also measure the total resistan"e o the "ir"uit a"ross the terminals ; H )
.sin% the &ina (ro pro%ram to simulate the "ir"uit shon in Gi%ure 1 an$ "han%e the resistan"e values use$ in the experiment) &hen, re"or$ the simulate$ $ata rom the pro%ram to "omplete the $ata in &ale 3)2 III) +ES.&S ;- -ISC.SSI Experiment no) 3 $eals ith the anal'sis o resistive netors usin% 0ir"hho9s las) ; seriesFparallel "ir"uit as "onstru"te$ hi"h "ontains ive resistors) &he "urrent loin% throu%h an$ the volta%e a"ross ea"h resistor ere measure$)
&;E I Measure$ values
Gi%ure 3: ;mmeters ere use$ to $etermine the "urrent at $ierent ran"hes o the "ir"uit) .sin% the B))M), to measure the volta%e rea$in%s passe$ throu%h ea"h resistors o the "ir"uit an$ usin% the ammeter to measure the "urrent loin% at $ierent ran"hes o the "ir"uit)
+ 1
32)1
B1
!)K B
I1
1! m;
+ 2
L66)2
B2
1!)A2 B
I2
1! m;
+ 3
L6)2
B3
1)2!7 B
I3
12)3 m;
+ !
K2
B!
A)L71 B
I!
1)! m;
+ 7
21K)
B7
A)3A B
I7
1)! m;
+ &
1!A7
B&
2A B
I&
1! m;
&ale I shos the measure$ values o the volta%e a"ross an$ the "urrent loin% throu%h ea"h resistor) ase$ rom the values otaine$, it "an e anal'se$ that + ! an$ + 7 are resistors in series sin"e the same "urrent is loin% throu%h them) &he "omination o these to resistors is in parallel ith + 3 e"ause the sum o B! an$ B7 is approximatel' equal to B3) ;lso, the "omination o + !, + 7 an$ + 3 is in series ith + 1 an$ + 2 sin"e the sum o B1 B2 an$ B3 is equal to the volta%e sour"e)
&;E II "al"ulate$ values
+ 1
+ 2
+ 3
+ !
+ 7
333)K
1AA1)!3
1A1)22
KL)2L
21L)2L
+ &
I at C
;C- ;
CEG-C
;CEG- ;
1!26)7
A)3 m;
A)AK7 B
FA)A13 B
A)A72 B
&ale II shos the "al"ulate$ values o the resistan"e hi"h are otaine$ usin% hm9s la) It "an e seen that oth the measure$ an$ "al"ulate$ values or resistan"e a%ree) &his su%%ests that the resistan"e "an e "al"ulate$ on"e the volta%e an$ "urrent are non) Grom tale II, it as shon that I at C is approximatel' equal to zero) In tale I, it "an e noti"e$ that I1 is approximatel' equal to the sum o I3 an$ I! hile I2 is approximatel' equal to the sum o I3 an$ I7) &hese prove that the summation o all "urrent ithin a %iven no$e is equivalent to zero hi"h is non as 0ir"hho9s "urrent la) Similarl', the sum o the "urrents enterin% a no$e is equal to the sum o "urrents leavin% the no$e) &his shos that the "har%e in ele"tri" "ir"uits is "onserve$) Gurthermore, in tale II, the values o B at loops ;C-;, CEG-C an$ ;CEG-; are approximatel' equal to zero) &his veriies that the summation o volta%e aroun$ a loop in a "ir"uit is equivalent to zero hi"h is non as 0ir"hho9s volta%e la) Grom tale I, the sum o B 1 B2 an$ B3 is approximatel' equal to B& an$ the sum o B! an$ B7 is approximatel' equal to B3) &his means that the sum o volta%e rise is equal to the sum o volta%e $rop aroun$ a "lose$ path or loop) Sin"e volta%e is or over "har%e, this shos that ener%' is also "onserve$ in ele"tri" "ir"uits)
&;E III Simulate$ values
+ 1
32)1
B1
!)KK B
I1
1! )27m;
+ 2
L66)2
B2
1!)A6 B
I2
1! )27m;
+ 3
L6)2
B3
1)2K B
I3
12)63 m;
+ !
K2
B!
A)L72 B
I!
1)! 2m;
+ 7
21K)
B7
A)3A B
I7
1)! 2m;
+ &
1!AA
B&
2A B
I&
1!)27 m;
&ale III shos the simulate$ values otaine$ usin% &ina (ro sotare in the "omputer) It "an e seen that oth the measure$ an$ simulate$ values a%ree)
IB) CC.SI In this experiment, e use the same "ir"uit e use in experiment to ithout the use o ohm9s la ut usin% 0ir"hho9s la) &he 0ir"hho9s las ollo the la o "onservation o ener%' in a "ir"uit) &he Bolta%e la an$ "urrent la state that the amount ener%' enterin% is also the amount o ener%' leavin%) Even ithout the nole$%e o ohm9s la, the volta%e an$ "urrent "an e "ompute$ manuall' usin% summation) 0ir"hho9s las are useul espe"iall' hen anal'zin% "ompli"ate$ "ir"uits that are not "overe$ ' the hm9s la) .sin% the to as e "an solve or unnon resistan"e "urrent an$ also volta%e) ;C0NE-/EME& &his laorator' report oul$ not e possile ithout the %ui$an"e an$ the help o the in$ivi$uals ho in one a' or another "ontriute$ an$ exten$e$ their valuale assistan"e in the preparation an$ "ompletion o this report) Ne oul$ lie to express our $eepest %ratitu$e to our "lass mentor, (ro) (aulo &in$o%an or his %ui$an"e an$ tea"hin%s $urin% the experiment) De helps us to "on$u"t the experiment or us to no hat to $o)
Ne oul$ also lie to %ive thans to our ello "lassmates or their support an$ help) ;n$ lastl', e express our $eepest thans to ;lmi%ht' /o$ or Dis lessin%s an$ %ui$an"e in our lie) +EGE+ECE 415
O/ustav +oert 0ir"hhoP, last mo$iie$ ;u%ust 2AA2, http:Fhistor')m"s)stF an$res)a")uio%raphies0ir"hho)html 425
Carlos C) Dortinela IB an$ /or%onio C) Ballestero II, Elementar' Ele"tri"al En%ineerin% Manual
