electrical calculations for electric.pdf

electrical calculations

1. Alegerea conductoarelor si cablurilor electrice







Preambul

R aco rdarea la re ţeau a electrică a consum atorilor se realizeaz ă du p ă normativ u l NTE 007/08/00 care
în locuie ş te PE 107/95
https://www. anre.ro/downlo ad. php?f= f61%2Bgw%3D%3D&t= vdeyut7d lce crLbbvbY%3D
Pen tru aplica ţ ii m ai re duse ca ş i complexitate am re alizat un ghid care d ore ş te s ă ajute în alegerea
sec ţ iu nii cond uctoare lor d ar care s ă ş i explice lo cul ş i rolul consumatorului racordat în sistem.
Pen tru calcul e rap id e exist ă variante de programe o nline . Iproeb SA are un astfel de calculato r online la
adre sa http s://ipro eb .ro/resu rse/fcc/dc. htm
Calculele dup a gh id ul de m ai jos se fac pentru cazurile în care nu se reg ă sesc în set ă rile aplica ţ ie i sau ca
în c ă o verificare a unor rezultate .
Bine în ţ eles c ă acest ghid este orientativ, perfectibil ş i poate fi updatat. Este conceput pentru
alim entare a con sum atorilor de JT . Pen tru co ntribu ţ ii n e p ute ţ i scrie pe adresa m [email protected]


Pen tru a realiz a şi cole tajul ( tip şi num ăr de tam buri ) am d ezvoltat o aplicaţie online la adre sa
https://iproeb.ro/resurse/tamb/dc.htm

2. !"#"$$%&'()*$$!"+"$$*%!,'%,+$$-$.+*'%#+$/)$#+*01'%$%2(0+,)
34%/$/)$+0)3)')$+$!)#,%15%%
#(5/1#,(+')0('$)0)#,'%#)
%67"$*869:$/;6<
=$%>?@8A$!+$BCCB

3. !"#$%&'()*+,-((#.*&*+,/*#,'01+,#+*-*/*/%+#)*#)('-+(20-(*#)*#3%,',#-*&'(0&*
!"!#$%&'()(*&+,&##+,-,%,%.+#,%,*-+(*,#/,#/('-+(01-(,#/,#2.&'&#-,3'(13,"#4,)(3(-((5#-,+6(3.%.7(,"
4(3# 813*-# /,# 9,/,+,# *.3'-+1*-(95# +,-,%,%,# ,%,*-+(*,# /,# /('-+(01-(,# /,# 2.&'&# -,3'(13,# :&9&3/# -,3'(13,&
3.6(3&%&#(3-+,#)&;,#/,#<=>?@#',#(68&+-#(3#1+6&-.&+,%,#*&-,7.+((A# B%(3((#,%,*-+(*,#&,+(,3,C
B%(3((#,%,*-+(*,#'10-,+&3,"
D(3((%,#,%,*-+(*,#&,+(,3,#',#(68&+-#%&#+&3/1%#%.+#(3#1+6&-.&+,%,#*&-,7.+((A
B%(3((#,%,*-+(*,#&,+(,3,#*1#*.3/1*-.&+,#3,(;.%&-,#:#'.%1-(,#*%&'(*&#@C
B%(3((#,%,*-+(*,#&,+(,3,#*1#*.3/1*-.&+,#(;.%&-,#+&'1*(-,#(3#)&'*(*.%#:-.+'&/&-,@"
4(3#813*-#/,#9,/,+,#&%#)13*-(.3&%(-&-((5#+,-,%,%,#,%,*-+(*,#/,#/('-+(01-(,#/,#2.&'&#-,3'(13,#',#(68&+-#(3
1+6&-.&+,%,#*&-,7.+((A
B+,-,%,#8,3-+1#&%(6,3-&+,&#(%16(3&-1%1(#810%(*C
B+,-,%,#8,3-+1#&%(6,3-&+,&#*.3'16&-.+(%.+#(3/1'-+(&%(C
B+,-,%,#8,3-+1#&%(6,3-&+,&#*.3'16&-.+(%.+#*&'3(*(C
B#+,-,%,#8,3-+1#&%(6,3-&+,&#*.3'16&-.+(%.+#*&'3(*(#'(#&#(%16(3&-1%1(#810%(*
B0+&3'&6,3-,#,%,*-+(*,#:#&,+(,3,#'&1#'10-,+&3,@"
E3#*&;1%#%(3((%.+#,%,*-+(*,#&,+(,3,5#6.3-&+,&#*&0%1+(%.+#',#)&*,#8,#'-&%8(#'&1#8,#)&-&/,%,#*%&/(+(%.+5#6./1%
/,#6.3-&+,#)((3/#'8,*()(*#-(81%1(#/,#*&0%1#&%,'#:(;.%&-5#3,(;.%&-@5#(&+#(3#*&;1%#%(3((%.+#,%,*-+(*,#'10-,+&3,5#/('-+(01-(&
,3,+7(,(#,%,*-+(*,#',#+,&%(;,&;&#8+(3#*&0%1+(5#8.;&-,#/,#+,71%&#'10#-+1-1&+,#%&#.#&/&3*(6,#/,#**&"#>"=#6,-+(5#(3&/(+(%,
'&1#/,+(9&-((%,#)&*&3/1B',#8+(3#(3-,+6,/(1%#6&3'.&3,%.+"
4,%(6(-&+,&#/(3-+,#+,-,&1&#,%,*-+(*&##/,#/('-+(01-(,#'(#(3'-&%&-(&#(3-,+(.&+&#&#&0.3&-1%1(#',#)&*,#/,#%&
0.+3,%,#/,#(,'(+,#/(3#*.3-.+1%#/,#,3,+7(,#,%,*-+(*&"#F&3&#%&#0.+3,%,#/,#(,'(+,#/(3#*.3-.+1%#/,#,3,+7(,#,%,*-+(*&#5
)1+3(;.+1%#/,#,3,+7(,#&+,#.0%(7&-(&##/,#&#(3-+,-(3,#+,-,&1&#/,#/('-+(01-(,#'(#&'(71+&+,&#%&#0.+3,#&#*.3/(-((%.+#/,
)1+3(;&+,#*.3-+&*-1&%,#:#81-,+,#(3'-&%&-&#%&#)+,*9,3-&#'(#-,3'(13,&#(3#%(6(-,%,#&/6(',@"
/8D;6;9;;E$98?F;6@G@7;8 "#F+(3*(8&%,%,#3.-(13(#&1#1+6&-.&+,%,#',63()(*&-((A
G,3'(13,&#3.6(3&%&#&#+,-,%,(#:H3@5#,'-,#-,3'(13,&#8+(3#*&+,#+,-,&1&#,'-,#/,316(-&#'(#%&#*&+,#',#)&*,
+,),+(+,#8,3-+1#&316(-,#*&+&*-,+('-(*(#/,#)13*-(.3&+,#&#+,-,%,("
G,3'(13,&#/,#',+9(*(1#&#+,-,%,(#:H'@5#,'-,#-,3'(13,&#(3-+,#/.1&#)&;,#&%,#13,(#+,-,%,#,%,*-+(*,5#(3-+B13
&316(-#813*-#'(#%&#13#6.6,3-#/&-"
I0&-,+,&#8+.*,3-1&%&#&#-,3'(13((#/,#',+9(*(1#)&-&#/,#-,3'(13,&#3.6(3&%&5#,'-,#/,)(3(-&#8+(3#+,%&-(&A
n
n s
U
U U
a
−
=
%
J8+,#,K,68%()(*&+,5#*.3).+6#JGIJ#L<>BMN5#&0&-,+(%,#8+.*,3-1&%,#&/6('(0(%,#8,3-+1#&7%.6,+&+(#*1#6&(
81-(3#/,#!>>>#%.*1(-.+(#'13-#/,#O!>P5#(&+#8,3-+1#&7%.6,+&+(#*1#6&(#61%-#/,#!>>>#%.*1(-.+(#/,#OMP"
!"4"#(56789:;<7#:=>578;?=8;5;@787A#9B7C=A#9D:;<7C9:77A#6;8D@=5:9:77#E<=F9:7:;9<="
D&#0&;&#,K,*1-&+((#+,-,%,%.+#/,#/('-+(01-(,#'(#&%(6,3-&+,#&#+,*,8-.+(%.+5#)(,#*&#,'-,#9.+0&#/,#%1*+&+(#3.(
'&1#/,#+,*.3'-+1*-((#+,-,%,5#-+,01(,#'&#,K('-,#/.*16,3-&-((#/,#8+.(,*-&+,"
4.*16,3-&-(&#131(#8+.(,*-#/,#,K,*1-(,#*.3-(3,#.#8&+-,#'*+('&5#.#8&+-,#/,',3&-&#'(#9.%16,#'8,*(&%,"
F&+-,&#'*+('&#*18+(3/,5#/,#+,71%&A
B21'-()(*&+,&#3,*,'(-&-((#%1*+&+((C
B(3*&/+&+,&#(3#(3/(*((#/,#*.3'16#3.+6&-(C
B0+,9(&+,#/,#*&%*1%#,%,*-+(*,#'(#6,*&3(*,C
B7+&)(*,#/,#,'&%.3&+,#&#%1*+&+(%.+C
B&9(;,#'(#&*.+/1+(C
B/,9(;,5#&3&%(;,#/,#8+,-1+(C
B%('-&#/,#,*Q(8&6,3-,#'(#6&-,+(&%,"
F&+-,&#/,',3&-&#*18+(3/,5#/,#+,71%&A
B8%&31%#/,#'(-1&-(,#(3#&3'&60%1C
B8%&31+(#/,#'(-1&-(,#(3#/,-&%(1C
B'*Q,6&#,%,*-+(*&#*1#(3*&/+&+,&#(3#'('-,6#:'(-1&-(&#,K('-,3-&#'(#'(-1&-(&#9((-.&+,@C
B8%&3',#/,#/,-&%((#8+(9(3/#+,&%(;&+,&#+,-,%,("
?.%16,%,#'8,*(&%,#*18+(3/5#/,#+,71%&A
B/.*16,3-&-((#8,3-+1#'*.&-,+,&#/(3#*(+*1(-1%#&7+(*.%C
B/.*16,3-&-((#8,3-+1#/,'8&710(+(C
B/.*16,3-&-((#-,Q3(*,#8,3-+1#-+&',,#'8,*(&%,#:#(3*+1*('&+(#*1#%(3((#/,#-,%,*.613(*&-((5#*&(#),+&-,5
'.',%,#,-*"@"
D&#,%&0.+&+,&#131(#8+.(,*-#/,#,K,*1-(,#-+,01(,#'&#',#8&+*1+7&5#(3#7,3,+&%5#1+6&-.&+,%,#,-&8,A
B&3&%(;&#-,6,(#/,#8+.(,*-&+,C
B*.3)+13-&+,&#/&-,%.+#/(3#-,6&#*1#'(-1&-(&#/(3#-,+,3C
B,),*-1&+,&#6&'1+&-.+(%.+#/,#-,+,35#(3#;.3&#(3#*&+,#1+6,&;&#&#',#*.3'-+1(#+,-,&1&C
B'-&0(%(+,&#9&+(&3-,%.+#/,#+,&%(;&+,#&#+,-,%,(C
B,),*-1&+,&#*&%*1%,%.+#/,#/(6,3'(.3&+,#&#+,-,%,(C
B,%&0.+&+,&#/.*16,3-&-((%.+#3,*,'&+,#8,3-+1#.0-(3,+,&#&9(;,%.+#'(#&*.+/1+(%.+"
!"G"#$;567:77#6=#89H7:9:=#75#9H7@=5:9<=9#8D#=5=<F7=#=H=8:<789#9#8;5ID@9:;<7H;<"
$.3/(-((%,#/,#*&%(-&-,#',#+,),+&#%&#9&%.+(%,#-,3'(13((5#)+,*9,3-,(5#81-,+((#'(#*.3-(31(-&-((#&/6(',#8,3-+1
.#013&#)13*-(.&3+,#&#+,*,8-.&+,%.+"
:"$,86H;<68:#*.3'-&3-&5#*&#9&%.&+,#'(#).+6&5#*.3'-(-1(,#.#8+(6&#*.3/(-(,#8,3-+1#.+(*,#-(8#/,
+,*,8-.+"
E3#,K8%.&-&+,&#(3'-&%&-((%.+#,%,*-+(*,#&8&+##9&+(&-((#/,#-,3'(13,#*&1;&-,#/,#*.3'16&-.+5
9&+(&-((#%,3-,#/&-.+&-,#9&+(&-((%.+#/,#'&+*(3&#'(#9&+(&-((#+&8(/,#/&-.+&-,#'*1+-*(+*1(-,%.+#'&1#6./()(*&+(%.+#+&8(/,
/,#'&+*(3&"
H3#7.%#/,#-,3'(13,#',#/,)(3,'-,#8+(3#'*&/,+,&#9&%.+((#,)(*&*,#&#-,3'(13((#13,(#+,-,%,
,%,*-+(*,#*1#.#&68%(-1/(3,#*18+(3'&#(3-+,#.#9&%.&+,#6(3(6&#','(;&0(%&#:>5RH3@#'(#H3#'(#.#/1+&-&#/,#*,%#61%-#<
',*13/,"#4,#+,6&+*&-#*&#'13-#61%-,#+,*,8-.&+,#',3'(0(%,#%&#7.%1+(#/,#-,3'(13,"
I0&-,+,&#/,#%&#).+6&#'(31'.(/&%&#&#13/,(#/,#-,3'(13,#/,-,+6(3&#)13*-(.3&-,&
+,*,8-.&+,%.+#/,#*1+,3-#&%-,+3&-(9#(3#+,7(6#/,).+6&3-"#J,#/,)(3,'-,#&'-),%#*.,)(*(,3-1%#/,#/('-.+'(13,# δδδδ
D
#*&
+&8.+-1%#/(3-+,#9&%.&+,&#,)(*&*,#&#+,;(/11%1(#/,).+6&3-#H/#'(#9&%.&+,&#,)(*&*,#&#13/,(#/,#-,3'(13,5
9&%.&+,&#*.,)(*(,3-1%1(#/,#/('-.+'(13,#)((3/#/,#>5>=#8,3-+1#2.&'&#-,3'(13,#'(#6,/(,#-,3'(13,#'(#/,
>5><#8,3-+1#(3&%-&#-,3'(13,"
A"$.?8IJ869:#*.3'-&3-&#&#-,3'(13((#/,#&%(6,3-&+,#*.3'-(-1(,#13#-,%#6&2.+#&-&-#8,3-+1#013&
)13*-(.3&+,#&#+,*,8-.&+,%.+5#6,3-(3,+,&#8+,*(;(,(#&8&+&-,%.+#/,#6&'1+&#*&-#'(#8,3-+1#6&'(3(%,#/,#%1*+1
&3-+,3&-,#/,#6.-.&+,#/,#*1+,3-#&%-,+3&-(9"
I0&-,+(%,#6&K(6,#&/6(',#&%,#)+,*9,3-,(#:##########@'13-#/,# ±>"NS;"
I"$!;F89?;:$986H;<6;G@? "
$&1;,%,#3,'(6,-+(,(#'13-#(3#*,&#6&(#6&+,#8&+-,#'&+*(3(%,#/,;,*Q(%(0+&-,#&%,
*.3'16&-.+(%.+"#T,'(6,-+(&#-,3'(13(%.+#',#,K8+(6&#8+(3-+B13 *.,)(*(,3-#/,#3,'(6,-+(,5
/&-#/,#+,%&-(&A
13/, I
EB#*.68.3,3-&#(39,+'&
I
/
B#*.68.3,3-&#/(+,*-&
9&%.&+,&#&**,8-&-&#&#3,'(6,-+(,(#)((3/#6&(#6(*&#/,#RP"
f
adm
∆
k
ds%
U
n
i
U
i
U
Ud
u
∑
=
= =
2
2
δ
100
%
⋅ =
d
i
ds
A
A
k

4. Inalta tensiune IT
Medie tensiune
MT
Joasa tensiune JT
SSE
ST
(
SD
)
PTPT
m
i
m
j
TGTG
TD
TU
1
22
3
45
5
55
Fig. 1 - Compunerea instalatiilor electrice la consumator
K"$&<98?8:$I8?<9:#:3,*,'&+&@#,'-,#.#*.3/(-(,#7%.0&%&#(3#8+.(,*-&+,&#'(#,K8%.&-&+,&#*.3'16&-.+(%.+"#E3
)13*-(,#/,#81-,+,&#*,+1-&#'(#/,#-,3'(13,&#6(3(6&#(3#813*-1%#/,#+&*.+/#',#/,)(3,'*#8&-+1#*%&',#/,#*.3'16&-.+(A
8"$#@69;6<;9:98:$;6$:G;F869:?8 #*.3'-(-1(,#*,&#6&(#(68.+-&3-&#*.3/(-(,#*&%(-&-(9&"#E3#)13*-(,#/,#3&-1+&
,),*-,%.+#8+./1',#/,#(3-+,+18,+,&#&%(6,3-&+((#*1#,3,+7(,#,%,*-+(*&5#&9,3#8&-+1#*&-,7.+((#/,#+,*,8-.&+,A
B*&-,7.+(&##UA#B3,&%(6,3-&+,&#/1*,#%&#,K8%.;((5#(3*,3/((5#8(,+/,+(#/,#9(,-(#.6,3,'-(C
B*&-,7.+(&##EA#B3,&%(6,3-&+,&#/1*,#%&#/,+,7%&+,&#8+.*,',%.+#(3#)%1K#*.3-(311#'(#(3#)(3&%#%&
8&710,#3,+,*18,+&0(%,C
B*&-,7.+(&#EEA#B8&710,%,#6&-,+(&%,#8+./1',#/,#3,&%(6,3-&+,&#+,*,8-.+(%.+#'13-#+,*18,+&0(%,C
B*&-,7.+(&###EEEA#*18+(3/,#+,*,8-.&+,#*&+,#31#',#(3*&/+,&;&#(3#*&-,7.+((%,#8+,*,/,3-,"
4"#(&'-,/,-((#*/*$-+($*#/,#$%&'0J,-%+("
B"L"$%6H9:G:9;;$8G8I9?;I8$G:$I@6H<F:9@?;
$.3'16&-.+1%#/,#,3,+7(,#,%,*-+(*&#,'-,#&%*&-1(-#/(3#-.-&%(-&-,&#+,*,8-.&+,%.+#/(3-+B13#&316(-#'8&-(1#'&1
/(3-+B.#(3-+,8+(3/,+,"#I9&3/#(3#9,/,+,#*.+,%&-((%,#/,#3&-1+&#-,Q3.%.7(*&#/(3-+,#/(9,+',%,#%&-1+(##&%,#8+.*,'1%1(#/,
8+./1*-(,5#%&#*&+,#*.3*1+&#'(#(3'-&%&-((%,#,%,*-+(*,5#',#8.&-,#&)(+6&#*&#+,*,8-.&+,%,#,%,*-+(*,#'13-#%,7&-,#8+(3-+B13
'*.8#)13*-(.3&%"
E3'-&%&-((%,#,%,*-+(*,#%&#*.3'16&-.+#',#*.6813#/(3A
B+,*,8-.&+,#,%,*-+(*,C
B+,-,%,#,%,*-+(*,#'(#813*-,#/,#&%(6,3-&+,C
B,*Q(8&6,3-,#/,#*.3,*-&+,5#8+.-,*-(,5#IV$#,-*"5#&/(*&#+,'-1%#,*Q(8&6,3-,%.+#,%,*-+(*,#(3#&)&+&#/,
+,*,8-.&+,"
J*Q,6&#/,#/('-+(01-(,#7,3,+&%(;&-&#8,3-+1#(3'-&%&-((#,%,*-+(*,#%&#*.3'16&-.+#,'-,#8+,;,3-&-&#(3#)(71+&#!"
JJW B'-&-(&#'('-,61%1(#,3,+7,-(*C
JG:J4@ B'-&-(,#/,#-+&3').+6&+,#:/('-+(01-(,@C
FG B8.'-#/,#-+&3').+6&+,C
GX B-&0%.1#7,3,+&%#/,#/('-+(01-(,C
G4 B-&0%.1#/,#/('-+(01-(,C
GH B-&0%.1#/,#1-(%&2C
6
(
B+,*,8-.+#(3&%-&#-,3'(13,C
6
2
B+,*,8-.+#2.&'&#-,3'(13,C
! B+&*.+/#(3&%-&#-,3'(13,C
R B/('-+(01(-.+C
< B*.%.&3&C
Y B*(+*1(-#/,#1-(%&2C
N B*(+*1(-#/,#+,*,8-.+"
E3'-&%&-((%,#,%,*-+(*,#/,#2.&'&#-,3'(13,#+,&%(;,&;&#/('-+(01-(&#,3,+7(,(#,%,*-+(*,#%&
+,*,8-.&+,#(3/,8%(3(3/#&'-),%#'*.81%#)(3&%#&%#(3-+,71%1(#8+.*,'#/,#8+./1*,+,5#-+&3'8.+-#'(#/('-+(01-(,#&#,3,+7(,(
,%,*-+(*,"
Z&*.+/1%#+,*,8-.&+,%.+#'(#1-(%&2,%.+#%&#-&0%.1+(%,#/,#/('-+(01-(,#',#8.&-,#)&*,#+&/(&%#'&1#*1#%(3(,
8+(3*(8&%&"#$.3)(71+&-(&#+&/(&%&#:)(71+&#R@#,'-,#*,%#6&(#)+,*9,3-&#1-(%(;&-&#8,3-+1#+,-,%,%,#/,#/('-+(01-(,#/,#2.&'&
-,3'(13,"

5. TG
TS4
TS2
TS1
TS3
$.3,K(13,&#*1#%(3(,#8+(3*(8&%&#:)(71+&#<@#,'-,#6&(#)+,*9,3-#1-(%(;&-&#%&#+,&%(;&+,&#/('-+(01-(,(#(3
(3-,+(.+1%#1-(%&2,%.+"
X+18&+,&#+,*,8-.&+,%.+#'(#1-(%&2,%.+#8,#-&0%.1+(%,#/,#/('-+(01-(,#',*13/&+,#-+,01(,#'&#',#)&*&#(3#0&;&
1+6&-.&+,%.+#*.3'(/,+,3-,A
B,K('-,3-&#13.+#*.+,%&-((#)13*-(.3&%,#(3#*&/+1%#8+.*,'1%1(#-,Q3.%.7(*#/,',+9(-C
B&68%&'&+,&#(39,*(3&-&#(3#*&/+1%#',*-(,(C
B-&+()&+,&#(/,3-(*&#8,3-+1#*.3'161%#/,#,3,+7(,#,%,*-+(*&C
B%(8'&#8,+-1+0&-((%.+#+,*(8+.*,#'18&+&-.&+,#(3-+,#/(),+(-,#-(81+(#/,#+,*,8-.&+,C
B,9,3-1&%(-&-,&#13.+#%(6(-&+(#/,#81-,+,#/,#N[!>P#%&#*,+,+,&#)1+3(;.+1%1(5#(3#*&;#/,#/,)(*(-#/,#81-,+,#(3
'('-,61%#,%,*-+.,3,+7,-(*C
B+,*,8-.&+,%,#/,#*&-,7.+((#/(),+(-,#',#7+18,&;&#8,#-&0%.1+(#/(),+(-,"
!"#$%$&$'($)$&$&*('+$',&-%$.),($/
Z,-,%,%,#/,#&%(6,3-&+,#/,#2.&'&#-,3'(13,#8.-#)(#.+7&3(;&-,#*.3).+6#'*Q,6,%.+#/,#&%(6,3-&+,#&'-),%A
B'*Q,6,#+&/(&%,#:)(71+&#Y@C
B'*Q,6,#*1#%(3((#8+(3*(8&%,##:)(71+&#N@C
B'*Q,6,#01*%&-,##:)(71+&#\@C
B'*Q,6,#*.60(3&-,"
F,3-+1#&#&'(71+&#'(#.#+,;,+9&#(3#&%(6,3-&+,&#+,*,8-.&+,%.+#',#).%.','*#'*Q,6,#*1#+,;,+9,#(3#*&(#/,
&%(6,3-&+,#:)(71+&#M#&@5#'*Q,6,#*1#+,;,+9,#(3#'1+',#:)(71+&#M#0@#'(#'*Q,6,#*1#+,;,+9&#(3#*&(#/,#&%(6,3-&+,#'(#(3
'1+',#:)(71+&#M#*@"
TD
M3 M3
m1
u1
u2
u3
m2
u4
TD
Fig. 2 – Schema de distributie
radiala aferenta tabloului TD
M3
M3
m1 u1 m2
Fig. 3 – Schema de distributie cu linie principala
TD
utila
j
e si
TS1
TS1’
TS2
TD TS4
TS3
TS2’
TG
TS1
TS2
TS3
TS4
TS5
TS6
Fig.
Fig.
Fig.
TG
TD2
TD1
TD3TGTG
PTPT
LELE
TD
PT
PT
LELE
LP
LP
Fig. 7 – Asigurarea rezervelor in alimentarea
abc

6. 4"4"#1<;:=8:77H=#<=:=H=H;<#6=#67I:<7KD:7="
Z,-,%,%,#/,#/('-+(01-(,#-+,01(,#8+,9&;1-,#*1#8+.-,*-((#&%,#+,-,%,(#'(#*.3'16&-.+(%.+"
F+.-,*-(&#(68.-+(9&#*1+,3-(%.+#/,#'*1+-*(+*1(-#&+,#',63()(*&-(&#13,(#8+.-,*-((#&#+,-,%,%.+#/,.&+,*,#316&(
&*,'-,&#'13-#'.%(*(-&-,#%&#'*1+-*(+*1(-"#F+.-,*-(&#+,*,8-.&+,%.+#%&#'*1+-*(+*1(-#,'-,#3,',63()(*&-(9&#/,.&+,*,
/,),*-,%,#+,*,8-.&+,%.+#'13-#*&1;,%,#'*1+-*(+*1(-,%.+"
F+.-,*-(&#(68.-+(9&#*1+,3-(%.+#/,#'18+&'&+*(3&#&+,#',63()(*&-(&#13,(#8+.-,*-((#&#+,*,8-.&+,%.+"
$,%,%&%-,#8+.-,*-((#*&+,#',#6&(#8+,9&/#'13-#/,'-(3&-,#+,*,8-.&+,%.+#8,3-+1#&#(6813,#6./1%#/,#%1*+1#:
8+.-,*-(&#(68.-+(9&#%(8',(#-,3'(13((#/,#&%(6,3-&+,#'&1#&#'*&/,+((#&*,'-,(&5#8+.-,*-(&#*.3-+&#6&+(+((#,K&7,+&-,#&
-1+&-(,(5#8+.-,*-(&#*.3-+&#)13*-(.3&+((#(3#/.1&#)&;,@"
G"#)(J*&'(%&,+*,#+*-*/*/%+#*/*$-+($*"
$9H8DHDH#I=8:7D577#8;56D8:;9<=H;<#E=5:<D#87<8D7:=H=#6=#<=8=E:;<"
J,#/,-,+6(3&#*1+,3-1%#*,+1-#/,#+,*,8-.+#/18&#13&#/(3#+,%&-((%,A
E3#8+&*-(*&#*&%*1%1%#',*-(13((#',#)&*,#8+(3#*&%*1%1%#*1+,3-1%1(#*,+1-#/,#+,*,8-.+5'(#&8.(#(3#)13*-(,#/,
9&%.&+,&#.0-(31-&#',#(&#/(3#-&0,%#9&%.&+,&#',*-(13((#*.3/1*-.&+,%.+"418&#3&-1+&#+,-,%,%.+#,%,*-+(*,:(3-#'&1
,K-@5*&%*1%1%#/,#/(6,3'(.3&+,##',#(3*,8,#5)(,#(3#)13*-(,#/,#(3*&%;(+,&#&/6('&#&#*.3/1*-.+1%1(5)(,#(3#)13*-(,#/,
8(,+/,+,&#/,#-,3'(13,"G+,01(,#'&#',#-(3&#',&6&#/,#3&-1+&#+,*,8-.&+,%.+#1-(%(;&-,"E3*&%;(+,&#8+(3#,),*-#-,+6(*
/,8(3/,#/,#+,7(61%#/,#%1*+1#A#8,+6&3,3-5(3-,+6(-,3-#'&1#/,#'*1+-&#/1+&-&"E3#+,7(6#8,+6&3,3-#5*1+,3-1%#6&K(6
&/6('(0(%#/,8(3/,#/,#*&+&*-,+('-(*(%,#6&-,+(&%1%1(#:7,.6,-+(*,5/,#-+&3'6('(,#&#*&%/1+((@"E3#+,7(6#(3-,+6(-,3-
*1+,3-1%#6&K#&/6#/,8(3/,#(3#8%1'#'(#/,#/1+&-&#+,%&-(9&#/,#*.3,*-&+,"E3#*&;1%#+,7(61%1(#/,#'*1+-&#/1+&-&:/,#,K#%&
8.+3(+,&#6.-.&+,%.+@5*1+,3-1%#6&K#&/6('(0(%#/,8(3/,#/,#-(81%#'&+*(3((#'(#/,#*.3/(-((%,#/,#)13*-(.3&+,
:(3*&%;(+,5',+9(*(1@"
$9H8DHDH#I=8:7D577#E=5:<D#<=8=E:;9<=#6=#HD@759 #A
!@#I%,7,+,&#'(71+&3-,(#)1;(0(%,##-+,01(,#)&*1-&#&'-),%#(3*&-#',*-(13,&#*.3/1*-.+1%1(#'&#)(,#&'(71+&-&"]1;(0(%1%
-+,01(,#'&#'18.+-,#*1+,3-1%#3,*,'&+#+,*,8-.+1%1(#'&1#+,*,8-.&+,%.+#E*
E#)#^_#E*##513/,#E):*1+,3-1%#3.6(3&%#&%#'(71+&3-,(:I@@"F,3-+1#+,&%(;&+,&#8+.-,*-(,(#%&#(3*&+*&+,&#6&K#5E6&K#&8&+
1+6&-.&+,%,#'(-1&-((#A
B#(3'-&%&-((#(3#*&+,#8.-#&8&+,#'18+&'&+*(3(#*&3/##>5\E6&K#_`#E#)#_`#>5=#E6&K
B#(3'-&%&-((#)&+&#'18+&'&+*(3(#*&3/#E)#_#E6&K
$1+,3-1%#*,+1-#',#/,-,+6(3&#*1#1+6&-.&+,%,#+,%&-((A
E*#_#F(aH)b*.'#φ###13/,###F(#_##81-,+,&#(3#*(+*1(-:c@CH)#_#-,3'(13,&#/,#)&;&#:?@C*.'# φ#_#)&*-.+#/,#81-,+,
*.'#φ#_#>5LN##8,3-+1#)%1.+,'*,3-
*.'#φ#_#!#8,3-+1#(3*&3/,'*,3-
?&%.&+,&#3&-1+&%&#&#%1(#*.'# φ#,'-,#>5N#'(#',#(&#(3#*&%*1%#*&3/#31#',#-(3,#',&6&#/,#-(81%#(%16(3&-1%1("
B#*(+*1(-,#-+()&;&-,#,*Q(%(0+&-,:*1#'&+*(3(#'(6,-+(*,#8,#)&;,@#A
E*#_#Fa##<#H#*.'# φ####CH#d#-,3'(13,&#/,#%(3(,
B#*(+*1(-,#/,#&%(6,3-&+,#6.3.)&;&-,#A
E*#_#$'bF(a#H)b#*.'#φ#6C#$'#d#)&*-.+#/,#'(61%-&3,(-&-,5#*.'# φ#6#d#)&*-.+#/,#81-,+,#6,/(1##:>5LN"""!@
B#*.%.&3,#-+()&;&-,A
E*#_#$'bF(a###<#H#*.'# φ#6
$9H8DHDH#I=8:7D577#E=5:<D#<=8=E:;9<=#6=#L;<:9 #A
H3,%,#+,*,8-.&+,#,%,*-+(*,#&0'.+0#(3#&316(-,#+,7(61+(#/(3#)13*-(.3&+,&#%.+#*1#/1+&-,#+,%&-(9#+,/1',5
*1+,3-(#6&(#6&+(#/,*&-#*,(#3.6(3&%(5#316(-(#*1+,3-(#/,#9&+)"#I*,'-#)&8-#8.&-,#)(#.0',+9&-#%&#6.-.&+,%,#,%,*-+(*,
*&+,#%&#8.+3(+,#&0'.+0#13#*1+,3-#61%-#6&(#6&+,#/,*&-#*,%#3.6(3&%"#F,3-+1#&*,&'-&#'B&#'-&0(%(-#+,7(61+(#/,
8.+3(+,#&#6.-.&+,%.+#,%,*-+(*,"
F.+3(+,&#/(+,*-&#&#6.-.&+,%.+#,%,*-+(*,#,'-,#&/6('&#(3#1+6&-.&+,%,#*&;1+(A
B81-,+,&#6.-.&+,%.+#'&#31#/,8&',&'*&##R>P#/(3#81-,+,&#-+&3').+6&-.&+,%.+#)13*-(.3&3/#(3#8&+&%,%5#8,3-+1
*.3'16&-.+(#&%(6,3-&-(#8+(3#8.'-1+(#/,#-+&3').+6&+,#8+.8+((C
B',#9&#/,-,+6(3&#8,#0&;&#/,#*&%*1%#81-,+,&#6.-.&+,%.+#*&+,#8.-#)(#8.+3(-,#/(+,*-#(3#*&;1%#(3'-&%&-((%.+
&%(6,3-&-,#/,#%&#'1+',#,%,*-+(*,#8+.8+((5#9,+()(*&3/1B',#'&-(')&*,+,&#*.3/(-(,(#/,#8(,+/,+,#/,#-,3'(13,#&/6('&"
$.3/(-((%,#/,#8.+3(+,#&#6.-.&+,%.+#,%,*-+(*,#*1#81-,+(#6&(#6&+(#/,#Y#ec#(3*%1'(9#'&1#N5N#ec5#/18&
-,3'(13,&#/,#%(3(,#&#+,-,%,(#/,#RR>#?5#+,'8,*-(9#<=>?5#%&#*.3'16&-.+((#+&*.+/&-(#/(+,*-#%&#+,-,&1&#/,#2.&'&
-,3'(13,#&#)1+3(;.+1%1(5#',#'-&0(%,'*#/,#%&#*&;#%&#*&;5#8,#0&;&#13,(#&3&%(;,#(3#)&;&#/,#8+.(,*-&+,#-(3&3/#',&6&#/,
3&-1+&#*.3'16&-.+1%1(#'(#316&(#*1#&9(;1%#(3-+,8+(3/,+((#)1+3(;.&+,#/,#,3,+7(,"
$&%*1%1%#*1+,3-1%1(#*,+1-#A
B#*(+*1(-,#-+()&;&-,#A
E*#_#$(bFa###<#H#*.'# φ#3#C#13/,#F#_#81-,+,&#+,*,8-.+1%1(#:c@#CH#-,3'(13,&#/,#%(3(,:?@5$(#d#*.,)(*(,3-#/,
(3*&+*&+,:(3#)13*-(,#/,#-(81%#'&+*(3((@5*.'# φ#B##)&*-.+#/,#81-,+,
B#*(+*1(-,#6.3.)&;&-,#A
E*#_#$(bFaH)b#*.'#φ#6#5#13/,#F5*.'#φ#6#'13-#&*,%&'(#*&#6&(#'1'
B#(3#+,7(61%#/,#8.+3(+,#8,3-+1#9,+()(*&+,&#',*-(13((#.0-(31-,#',#*.68&+&#/,3'(-&-,&#/,#*1+,3-#,),*-(9&#*1#*,&#/,
8.+3(+,#A
E,)#_`#E#&/6
E&/6#_#E8a'#13/,#E8#d#*1+,3-1%#/,#8.+3(+,5'#d#',*-(13,&#(3#66#8&-+&-(
4,3'(-&-,&#/,#*1+,3-#&/6('&#,'-,#(3#)13*-(,#/,#3&-1+&#*.3/1*-.+1%1(#A
B#8-#*.3/#/,#$1###<N#Ia66#8&-+&-
B#8-#*.3/#/,#I%##R>#Ia66#8&-+&-
$&%*1%1%#*1+,3-1%1(#*,+1-:&#',*-(13((#3,*,'&+,@#',#8.&-,#)&*,#6&(#'(68%1#1-(%(;&3/#1+6&-.&+,%,#).+61%,#'(
9&%.+(%,#/(3#-&0,%#A
F_#Hb(5##E_FaH5##E*,+1-_F*,+1-&a$8bH#5#E*_#J*a$'bH##13/,
H#d#-,3'(13,&#/,#%(3(,:#<=>?#'&1#RR>?@#'&1#-,3'(13,&#*.3-(31&
$85$'#d#*.,)(*(,3-(#(3#)13*-(,#/,#316&+1%#+,*,8-.&+,%.+#8-#*&+,#',#*&%*1%,&;&#*1+,3-1%
*,+1-5',63()(*&-(&#81-,+((#'(#),%1%#&%(6,3-&+((#A
TU cr
m
1
TU - tablou de utilaj
cr -circuit de receptor
m
1
-receptor
Figura ______

7. T+#/,#+,*,8-.&+,
3_!5R5<#(/,3-(*,
J,63()(*&-(&#81-,+((#*,+1-,
G(8#&%(6,3-&+, $.,)(*(,3-
81-,+,#&0'.%1-& 81-,+,#1-(%&
3^Y
$8#<#*.'#φ3:#<#*.'#φ#3@bZ3 <#*.'#φ
-+()&;&-&
$' < <bZ3 <
$8*.'##φ3*.'#φ3bZ3 *.'##φ*
6.3.)&;&-&
$' ! Z3 !
** $8 ! Z3 !
$1+,3-1%#*,+1-#/,#)(,*&+,#+,*,8-.+#(3#8&+-,5',#'16,&;&#8,3-+1#.0-(3,+,&#*1+,3-1%1(#*,+1-#/,#R#'&1#<#+,*,8-.&+,
Z3##B#+&3/&6,3-1%#+,*,8-.+1%1(#35*.'# φ#(3/(*&-,#(3#*&;1%#6.-.&+,%.+58,#8%&*1-&#/,#(/,3-()(*&+,
#3#d#/,)&;&21%#-,3'(13((#/,#&%(6,3-&+,#8,3-+1#+,*,8-.+1%#3#: φ#_#>#58-#**@
$1+,3-1%#/,#8.+3(+,#E8#&#6.-.&+,%.+#*18%&-,#/(+,*-#%&#+,-,&',#/,-,+6(3&#*1#A
E8#_###λ##E3#5#13/,### λ#B#*1+,3-1%#+,%&-(9#/,#8.+3(+,#5#E3##B#*1+,3-1%#3.6(3&%#&%#6.-.+1%1(
λ#&+,#9&%.+(%,#A
\5N"""=##B##8,3-+1#6.-.&+,#&'(3*+.3,#*1#+.-.+1%#(3#'*1+-*(+*1(-
R"""R5N#B##8,3-+1#6.-.&+,#&'(3*+.3,#*1#+.-.+1%#0.0(3&-
<"""M###B###%&#8.+3(+,&#(3#&'(3*+.3#&#6.-.&+,%.+#'(3*+.3,
!5M"""R##B#8,3+-1#6.-.&+,#/,#**
E3#'(-1&-((%,#'8,*(&%,#/,#8.+3(+,#',#).%.','-,#*1+,3-1%#+,%&-(9#/,#8.+3(+,# λ!
λ!##_#λa<##%&#8.+3(+,&#'-,&#-+(137Q(
λ!#_#λafbf#d#%&#8.+3(+,#8+(3#&1-.-+&3').+6&-.+
λ!#_#λa!5R"""R##B#%&#8.+3(+,&#*1#+,.'-&-
(5:=5I7:MN7H=#@9O7@=#96@7I=#0",+%#9H=#8D<=5N7H;<#P5#<=F7@#E=<@95=5:##E=5:<D#8;56D8:=#D:7H7C9:=#P5
75I:9H9N77#L7O=A8D#7C;H9N7=#6=#1Q$#I9D#89D87D8AH9#:=@E=<9:D<9#@=67DHD7#9@K795:#6=#R4S#T$
E3-,3'(-&-,&#6&K(6#&/6('g#&#*1+,3-1%1(#5h3#I
$18+1 I%16(3(1
V.3-&-,#h3#-10#*i-, V.3-&-,#h3#-10#*i-,
J,*j(13,&
66
R
D(0,+,
h3#&,+R<YN5\
D(0,+,
h3#&,+R<YN5\
!R>!Y!R!!!>BBBBB
!5N RN !M !Y !< !! B B B B B R5N <Y RY R> != !\ RM != !\ !N !<
YYN<!R\RYR!<NR<R>!=!\ \NMY><Y<!RMYN<>RMRNR!
!> M= NN YL YN <L \! Y! <\ << RL !\ !>Y M< \Y N= N! =R NN YM Y< <= RN !<M !>> =Y M\ \M !>M MY \\ \> N< <N !\= !RN !>= L= =M !<R LN =< M\ \N N> R!> !N> !<N !R< !>Y !\N !!= !>< LY =R M> R\> R>> !M! !N\ !<M R>N !NN !<! !!L !>Y LN <!> RY! R!= !L= !MY RYN !=M !\\ !N! !<< !R> <\N RMR RN> RR= !L\ R=N R!M !L! !MY !N< !N> Y!N <!> R=> RNN RRY <<> R<= R!Y !LN !M! !=N YMN B B B B <MN B B B B RY> N\> B B B B YY> B B B B <>> \YN B B B B N!> B B B B Y>> MN> B B B B \>N B B B B
(5:=5I7:MN7H=#@9O7@#96@7I=#0",+%'9H=#8D<=5N7H;<#P5#<=F7@#E=<@95=5:#E=5:<D#89KHD<7#8D#7C;H9N7=#6=#1Q$
P5#@95:9#6=#1Q$
$&0%1+(#6.3-&-,#h3#8g6i3-#5%&#-,68,+&-1+&
6,/(1%1(#&60(&3-#/,#kR>$
$&0%1+(#6.3-&-,#h3#&,+#5%&#-,68,+&-1+&
6,/(1%1(#&60(&3-#/,#k<>$
$18+1#5*1 I%16(3(15#*1 $18+1#5*1 I%16(3(15#*1
J,*j(13,&
*.3/1*-.&+,%.+
66
R
!#*.3/1*-.+
:h3#*"*#@
R#*.3/1*B
-.&+,
<5Y
*.3/1*-.&+
,
!#*.3/1*-.+
:h3#*"*#@
R#*.3/1*B
-.&+,
<5Y#*.3/1*B
-.&+,
!#*.3/1*-.+
:h3#*"*#@
R#*.3/1*B
-.&+,
<5Y#*.3/1*B
-.&+,
!#*.3/1*-.+
:h3#*"*#@
R#*.3/1*B
-.&+,
<5Y#*.3/1*B
-.&+,
!5N <M <> RM B B B R\ R! != B B B R5N N> Y! <\ B B B <N RL RN B B B
Y\NN<Y\NRYR<\Y\<=<Y<\<>RM \=<\\N=\=NRYNN=Y=YYY\<=<Y
!> !!> == MM =\ \L \> => \\ \> \< NR YM !\ !Y> !!N !>> !!< L> M= !>N L> => =R M> \< RN !L> !N> !<> !N> !!N !>> !Y> !R> !>N !!> LY =R <N R<N !=> !NN !=> !Y> !R> !MN !N> !<> !<N !!N !>> N> R=> R!> !=N R!N !\N !YN R!N !=> !\> !\N !Y> !RN M> <N> R\> R<> RM> R>> !MN RM> R<> R>> R!> !=> !NN LN YR> <!N RMN <RN RYN R!N <NN RMN RYN R\> R!N !L> !R> Y=> <\> <!N <MN RMN RYN <L> <R> R=N <>> RN> R!> !N> NY> Y>> <NN YR> <!N RMN YYN <MN <RN <N> RL> RN> !=N \R> Y\> Y>> Y=> <NN <!> N!> Y<> <M> Y>> <<N R=N RY> MR> N<> Y\N N\> Y!N <\> \R> N!> Y<N Y=> <L< <Y> <>> =R> NL> NR> \Y> Y\N Y!> M!> NL> N>> NN> Y>> <L>
$&0%1#*1#13#*.3/1*-.+#1-(%(;&-#(3#'('-,6#-+()&;&-
J&+*(3&##&/6('(0(%&#/,#/1+&-&#:I@
F.;&+,#(3
8&6&3-5#%&
kR>
>
$
&,+5#%&
k<>
>
$
8&6&3-5#%&
kR>
>
$
&,+5#%&
k<>
>
$
J,*-(13,&
3.6(3&%&
66
R
$1 I% $1 I% $1 I% $1 I%
F.;&+,#(3#%(3(, F.;&+,#(3#-+,)%&
!5N B B RN B B B R> B R5N B B <Y B B B RM B
YBBYNBBB<MB \BBNMBBBY=B
!> B B M= B B B \\ B !\ !RM B !>< B !>M B =L B RN !\< B !<M B !<M B !!= B <N !LN !N! !\L !<! !\N !RM !YN !!< N> R<> !ML R>\ !\> !LN !N! !M\ !<= M> R=R R!= R\! R>R R<L !=\ RRY !MY LN <<\ R\! <R! RYL R=M RR< RM! R!> !R> <=R RLM <MY RL! <R\ RNY <!Y RYY !N> YR= <<R YR= <<< <\\ R=N <\! R=! !=N Y=< <M\ YLY <=Y Y!Y <R< Y!R <R> RY> N\! Y<M NL> Y\> Y=! <M= Y=Y <M= <>> \<R YLY \M= N<> NYR YRM NYL Y<< Y>> M<> NRM =!M \YR \RY YL\ \NM NR< N>> =R< \YL LY> MYY \L= N\R MYL \><

8. $&0%1#(3#*1+,3-#-+()&;&-
J&+*(3&##&/6('(0(%&#/,#/1+&-&#:I@
$&0%1#*1#<#'(#Y#*.3/1*-.&+, $&0%1#*1#N#*.3/1*-.&+,
F.;&+,#(3 F.;&+,#(3
8&6&3-5#%&#R>
>
$ &,+5#%&#k<>
>
$ 8&6&3-5#%&#kR>
>
$ &,+5#%&#k<>
>
$
J,*-(13,&
3.6(3&%&#&
*.3/1*-.+1%1(
66
R
$1 I% $1 I% $1 I% $1 I%
!5N R\ B !=5N B != B !Y B R5N <Y B RN B RY B !L B
Y YY<\<YRM<!RNR\R> \ N\YNY<<Y<L<R<RR\
!> MN \> \> YM N< YR YN <N !\ L= M= => \< \L NN \> YM RN !R= LL !>\ =< L> \L => \R <N !NM !!= !<! !>R !!> =< L= MM N> !=N !YR !NL !RY B B B B M> RR= !M\ R>R !N= B B B B LN RMN R!! RYY !L> B B B B !R> <!< RYR R=R RR> B B B B !N> <N< RM> <RY RNR B B B B !=N <LL <>= <M! R=L B B B B RY> Y\Y <\< Y<\ <<L B B B B <>> NRY Y!R Y=! <MM B B B B Y>> \>> YMN N\> YYY B B B B N>> B B B B B B B B
,H=F=<=9#87<8D7:=H;<#@;:;9<=H;<#9I758<;5=#:<7L9C9:=#8D#:=5I7D5=9#5;@759H9#6=#GUV#Q
F.+3(+,#/(+,*-&#%&#<=>#?
J
*&:&*-(9@
5#66
R
E
)5##I
]1;(0(%#*1#&+/,+,A$.3/1*-.&+, $&0%1
F3
fc
Z&8(/& D,3-&
E
'aE
-
:3.6(3&%a
+,7%&-@
I
$1 I% $1 I%
! R < Y N\M=
R>> B \<> Y>>a<=N B B RY> <>> !\> B N>> <R>a<!> B B !N> RY> !<R B Y>> RN>aRYN !R> B LN !N> !!> B Y>> RN>aR>N LN !N> LN !R> !>> B <!N R>>a!L> LN !R> M> LN
L> B <!N R>>a!M! M> !R> M> LN MN \<> <!N !\>a!N> M> LN N> M> NN N>> RN> !\>a!!! N> M> <N N> YN Y>> R>> !>>aLR <N N> RN <N Y> <!N R>> !>>a=R RN <N !\ RN <M R>> !\> !>>aMM RN <N !\ RN <> R>> !RN !>>a\Y !\ RN !\ RN RR !\> !RN \<aY= !> !\ !> !\
!="N !RN !>> \<aYR !> !\ !> !\
!N !>> => Y>a<N !> !\ !> !\ !! => \< <RaR\ \ !> \ !> M5N \< N> RNa!LY\Y\ N5N N> <N R>a!Y R5N Y R5N Y
Y <N RN !Na!! R5N Y R5N Y < RN RN !!aL R5NYR5NY
R5R RN R> =a\5N !5N R5N !5N Y !5N R> !\ \aY5= !5N R5N !5N Y !5! R> !> Y5Na<5= !5N R5N !5N Y
>5MN !\ !> <5<aR5= !5N R5N !5N Y >5NN !> \ R5YaR5R !5N R5N !5N Y >5<M \ Y !5=a!5\ !5N R5N !5N Y >5RN Y Y !5<a>5L !5N R5N !5N Y >5!= Y R !a>5M !5N R5N !5N Y >5!R R R >5MNa>5N !5N R5N !5N Y

9. F.+3(+,#lB∆#%&#<=>a\\>#?
J
*&
5#66
R
E
)5##I
]1;(0(%#*1#&+/,+,A$.3/1*-.&+, $&0%1
F3
fc
ZD
E
'aE
-
I$1 I% $1 I%
!R < YN\M=
R>> \<> N>> RN>aRRN !R> B LN !R> !\> N>> Y>> R>>a!=> LN !R> M> LN !<R N>> Y>> !\>a!YN M> LN N> M> !!> Y>> <!N !\>a!R> N> M> <N N> !>> <!N RN> !\>a!!> N> M> <N N>
L> RN> R>> !\>a!>> <N N> RN <N MN RN> R>> !>>a=M <N N> RN <N NN R>> !\> !>>a\Y !\ RN !\ RN YN !\> !RN \<aN< !\ RN !> !\ Y> !\> !RN \<aY= !> RN !> !\ <M !RN !>> \<aYN !> !\ !> !> <> !>> => Y>a<= !> !\ \ !> RR !>> => <RaR= \ !> Y \
!=5N \< N> <RaRY Y \ R5N Y
!N \< N> RNaR> R5N Y R5N Y !! N> <N R>a!N R5N R5N !5N Y M5N R< RN !Na!! !5N R5N !5N Y