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S3   ` ??"    }E 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDFF&dF  "p 0t"   0G3#" `r B T3??"`f  C 0Abottom logo"HB  s *޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B + Capsules  P  B(     6<f3#" `p  @ "  <G0*"pp  @   < "4    W#Click to edit Master subtitle style$ $vF     "  z"  B 6G3#" ` R r   Z3??#" `L  3   ` ??"   }E 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDFF&    ` ??"NnR  T Click to edit Master title style! !f  C 0Abottom logo"\  C &Acrown2"RB  s *޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B + 0,(  , , 0& P   t X*  , 0LTt    t Z*  , 6,Xt _P  t X*  , 6^t _  t Z* H , 0޽h ? 3380___PPT10.jipl @#(  x  c $& NnR & x  c $\& 0p   &   T& ?? 0   g)University of North Carolina at Charlotte"*(2*f3H  0޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B +.  0 "(   ~   s *pg&@  &   0 lA ?parallel: H $@  0 &  0 # 0e0eA  ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? H $@  0 &   THj& ??t@`,$ 0 The objective of resistor combination is to represent a complex network, composed of multiple series and parallel resistor combinations, with one equivalent resistance.X 2^8   Ts& ??,$ 0 Bparallel (2    Tv& ??p,$ 0 @series(2B    fDp?? p ,$@ 0B   # lDp?? p2 ,$@ 0B    fZDp??@ pp ,$@ 0B    fZDp??p pp ,$@ 0   T{& ??  ,$  0 Oequivalent resistance(2   \A(resistor3 <$@  0 &   TT& ?? p ,$  0 IReq* 2 H   0޽h ? 3f3fff̙3ff̙___PPT10+ךfD' = @B DS' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* ++0+ & ++0+ & ++0+ & ++0+ & ++0+ & +.  \T@ (  ~  s *&@  &   hASeries BunchP  <$@  0 &  T& ?? p,$ 0 4Req = R1 + R2 +R3 + & + Rn 2       T & ??0 PP ,$ 0 NR10 2%-  T( ??0 P ,$ 0 NR20 2%-  Tį& ??0  P ,$ 0 ^R3@ 2%- @ Tس& ?? 0 ,$ 0 ^Rn@ 2%-   T0& ?? p ,$  0 _Req@ 2%-B   # lDp??@ @ ,$@  0j   TȾ& ??0@6,$ 0 pTwo or more series resistors can be summed to represent an equivalent series resistance.&q lKqY   T& ??@h,$ 0 ]Resistors are in series if they are all in the same branch and are carrying the same current.(^0lKZ^  0 # 0e0eA.  ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?P  H $D  0 &H  0޽h ? 3f3fff̙3ff̙ME___PPT10%+> DI' = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(DQ' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwheel(4)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* ++0+& ++0+& ++0+& ++0+& ++0+& ++0+ & ++0+ & ++0+ & +85  ( P(  x  c $&@  &   lA parallel bunch <$@  0 & 0 # 0e0eA/  ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?ppH H $D  0 & @ T& ??0 P ,$ 0 ^Rn@ 2%-  T& ??0 `P ,$ 0 OReq0 2%-B  # lDp??  ,$@  0?  T& ??@,$ 0 OTwo or more parallel resistances can be combined by summing their conductances.P 2Pv   T& ??j@`p,$ 0 |Resistors are in parallel if they are connected across the same two nodes and share a common voltage across their terminals.&} lK}   T& ??0 0P ,$ 0 NR10 2%-   Tp ??0 pP ,$ 0 NR20 2%-   Tp ??0 ` P ,$ 0 ^R3@ 2%-   T p ?? 0,$  0 6or 2  T p ??` ,$ 0 6Geq = G1 + G2 + G3 + & + Gn 2      0 TA6 ? ? o@H $D  0 pH  0޽h ? 3f3fff̙3ff̙""___PPT10"+Ճ,D| ' = @B D7 ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwheel(4)*<3<*D8' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwheel(4)*<3<* D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwheel(4)*<3<*++0+p ++0+p ++0+p ++0+ p ++0+ p ++0+ p ++0+ p ++0+ p ++0+p +m(    `  (  r  S 5p@  p   T6p ??p pj ZContinued& *  2 f36  TL+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B+checkerboard(across)*<3<* D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B+checkerboard(across)*<3<* ++0+p ++0+p ++0+p ++0+p ++0+p ++0+ p ++0+p ++0+p +.  ''p"+'(   )0 # 0e0eA i ?A@ A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?p H i$D* 0 p ' T`p ??0  ,$. 0 ,Req = 1143  = 1.14 kr 2  %B # T`p ??0 . ,$ 0 TThis example can also be done using an alternative method. Let s keep the first answer we attained and compare that with the new answer we get using this alternative way. 2r  S |p@  p   T$p ??@,$ 0 Given: Consider the following resistive network pictured below where R1=2 k, R2=8 k and R3=4 k.d 2B %-% %  -  % %>K    fA) ? ?? 8 $@ 0W  TȠp ??p@,$  0 ;Find: The equivalent parallel resistance Req of the networkH< 2&   Tp ??P,$ 0 HR1* 2   T|p ?? ,$ 0 HR2* 2    Tpp ??P ,$ 0 HR3* 2    T\p ??@,$ 0 IReq* 2 B    `D8c??@@,$@  0    Tp ??` ,$  0 Q Solution 1:* 2     TPp ??` ,$  0 SUsing the conductance formula 2g  Tp ??  ,$  0 Geq = G1+G2+ G3 2    B   `D8c??P P P @ ,$@   0B   `D8c??P 00@ ,$@  0  T8p ??   < 2   c $A: ??p T 8 $D 0B   `D8c??P @ ,$@  0B   `D8c??P 0@ ,$D  0   fA0 ? ??P 008 $D 0  Tp ??`  ,$ 0 . Req = 1143  = 1.14 kr 2  %,   Tp ??0 0,$" 0 Q Solution 2:* 2    Thp ??0 ,$# 0 TUsing equ. 1 on previous slide 2   fAH ? ?? 0 @ 8 $D$ 0H  T,p ??@ 0 ` ,$& 0 Req1 = 1.6 k8 2    !  fAJ ? ?? ` 8 $@, 0 " T,p ?? @ ,$ 0 ,Req = 1143  = 1.14 kr 2  %A $ Tp ?? @p ,$/ 0 UNotice, both methods give us the same answer. Use the method you can easily remember.V 2V  & Tp ?? p ,$  0 Q Solution 1:* 2 2 (  ` >??"`P ,$D%  0 + Tt ?? ,$+ 0 JReq1* 2 H  0޽h ? 3f3fff̙3ff̙ii___PPT10i+DfDc' = @B Dc' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DD ' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(Dx ' =%(D< ' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DX' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(Dw' =%(D' =A@BB5BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*"D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*"D' =-g6B fade*<3<*"D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*#%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*)D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*)D' =-g6B fade*<3<*)D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =%(Df' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(++0+'t ++0+#t ++0+#t ++0+t ++0+t ++0+t ++0+t ++0+t ++0+ t ++0+ t ++0+ t ++0+ t ++0+ t ++0+ t ++0+ t ++0+t ++0+t ++0+t ++0+t ++0+t ++0+t ++0+t ++0+"t ++0+$t ++0+&t ++0++t +xrE{A&"`< *g&hԄ@PTqT]| |rIYz3-|3非NNwog263߆S!%X4y^>uhf7Hx,?,GV Jd,y 2A^D"K02 وlB^E6#[אב77[6m]d;ىBv#{>=d?r9 # m[Qd G"ǐ cd B rEN",%5r9\@AE.,fM wx~P6U0nhxoOxY%5y]Yd@Ղ5U8CB;.~ŭ_SwMjnqY%_sM?"wOL [̒o23vޝ˪G~>MʫW׺Ty~ݩCӣӓ/{4q6+Dv_MkݍQgGꊺo1c_tٿDsu;nl_?kƦm3'}Njs8̵r]'@rk9tu]vIfXe7ҵW);Abur8] )]F׽L-1r9ѵ)'3;Kr<  &O~ $،B̔MIbZJҒ~m>ຘkZt-]ˁ@rk9еTsv8{t]um3@U%. t-wBג1KkkD vv8'itt6U躺е|.t-ˁfrku39еmxTt-^#]K?sɁkrk.&t-ϵ ];Nt-]ˁ@rk9еZn qnS =`Nuitеad ɑ\[S] NwG@׶uk |s}:#I|uf>ؾ']X͠DB;@Tz*UFkxld#TM6KSuk*k[u%|&Clx xKsUG"bT|_'A&F|+(ZU)\ʍXVaV t댿;ܙtϴt9$ }N'/Oﮇ:ltgekvvӱ;[Or(9\y<_nJpy*/rDNKerC^!Wɫ5Zy^ o7ɛ-Vy]!w]Ny-{}r_> uvW3r|Tcq9+Oʧ䜜O<$ E|Y"_ku|S%ȷ;rQ+ߓGrϒw_"ls+y?Li|`{]?jg,IK#awGcM:[~1HwE_Cy??F~ѝP;]ep~;=ny⠕GbM%9dag'qVwڡ} +۞|6ן clKμFK:|^`>s8ٿY}Qsߎc9adjY]ٌ:3sңᯜUw."iuB-A `X mZ0h Zт[vmaSAMp G yZ(-zL,I oFݖB/ZhRF C>X ٳg Fi-Ov (-0h Z0h Z0h[p]ފQhXB=nV5eP럡VB %8AZh@AJZhQ%`ae E]BD 81dXh!2"h #iD?B #8A}Qw QQ~h!H-cwA \DcZM  wB Ai${д$p:Hi!H-CA"Ze +pDO=, m #TаB01_0h Z0h Z0h Z/BZVTMHvB0V V)%7n -wXFmaH${vL16F0sƆh <4xN@R p;l%TR!]HmUzZ<+ uekO[lÌ/3|s=rz2v~wB 80 ܳ=q]׿| }Ә>!zMC'Г)41Wk]x + 횷RK߿5֐,/s{;U>nt >eጩ}.lѧW}O%uEQ ji6Cugt<dƩt;EϿ/04aB>G_GevHoa.zlIIWJ㰰G%.ׁF?+vMk9qL m9qC=ondsF;J{,ۇqyWZPZGJܸ!+W\^(BAd*K ⊳_).S׌+҆DԀY.碸 7T.pW>k4I'\M4yRonoSS?W* poσ0~jn^JRʐaW0]0\V^{gpAWD%g1.5&Pq;v6xn@1(J*V$@* AT@)8A3<ܹ+6NdfN֙z?xGקϝߐ]!kp:VEP0V$!slϠϢk:k{(Ѻ}cXF_3Y]. 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