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P ,$@ 0B ??` @` ,$@  0B =X  fD>??p,$D  0H X 0޽h ? 3f3fff̙3ff̙((___PPT10c(.tS)+]ND'' = @B DJ'' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5X%(D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-6B+checkerboard(across)*<3<*XDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*6X%(D' =%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*8X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*8XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*8XD' =-g6B fade*<3<*8XDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*9X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*9XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*9XD' =-g6B fade*<3<*9XDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*:X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*:XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*:XD' =-g6B fade*<3<*:XDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*;X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*;XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*;XD' =-g6B fade*<3<*;XDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*7XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*7XD' =-g6B fade*<3<*7XDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*B ppt_w<*B ppt_h<*+B#style.visibility<*=X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*=XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*=XD' =-g6B fade*<3<*=X++0+5Xn ++0+6Xn ++0+7Xn +[  P\N(  \ \ ^A9"`<$@ 0 4x \ c $4@  4  \ ^A1"` k`^<$@ 0 4 \ T`4 ??N@ ,$ 0 "There will be some circuit symbols used in illustrations before they are properly discussed in this presentation. In order to prevent confusion, these symbols will be briefly introduced in this slide and later discussed in more detail. 2 \ C ,A resistor2"` ,$@$ 0 \ C &Asource"`!Y^,$@ 0 \ C (A source2"` $ ,$@  0  \ C &Aiground@ Z ,$@  0%  \ T$4 ??1 ,$ 0 mIdependent Voltage Source 2   \ T n ??0,$ 0 C Batteries 2 *  \ Tp"n ??P@p,$  0 r:Representations of voltage supplies used in this tutorial.;(2;  \ C (Ajsource3 @Z,$@  0 \ C (Aksource4"` 0 ,$@ 0  \ T(n ??0 @,$  0 SDependent Voltage Source 2D \ T4 ?? @ ,$ 0 PIndependent Current Source Dependent Current Source Q(2Q* \ T,n ??@0,$ 0 r:Representations of current supplies used in this tutorial.;(2; \ T 1??"`P,$D  0 \ T 1??"` ,$D 0 \ T\2n ?? ,$! 0 BGround (25 \ T3n ??*@J,$@" 0 }EGround is used as a reference and is typically at a 0 volt potential.F(2F \ T:n ??p D ,$% 0 DResistor (2 & \ Th>n ?? @@,$& 0 n6Resistors represent a hindrance to electrical current.7(27 \ T 1??"` P P ,$D' 0 \ T 1??"` ,$D# 0H \ 0޽h ? 3f3fff̙3ff̙DD___PPT10D.y+-D@' = @B Dh@' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(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<* \%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D~' =%(D&' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(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<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D*' =%(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' =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' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*\%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\F%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(D' =4@BBBB%(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<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(++0+\n ++0+\n ++0+ \n ++0+ \n ++0+ \n ++0+ \n ++0+ \n ++0+ \n ++0+\n ++0+\n ++0+\n ++0+\n ++0+\n ++0+\n ++0+\n ++0+\n ++0+\n +&    ` `T (  `~ ` s *pn@  n  ` RA9 @ <$D 0 na ` Trn ??j@p,$ 0 UVoltage is an electrical pressure which causes current to flow through a resistance. 8V 2T%!# ` TTyn ?? P ,$ 0 P (Batteries)( (2  ` T}n ??  ,$ 0 V(Independent Voltage Source)(2 ` Tn ??@ 0 ,$ 0 g/Two common DC voltage supplies are shown below:0 20 ` TTn ?? @,$  0 The  long side or + terminal of a battery is called the anode. B_ 2f3+   ` T n ??0@ P,$D 0 TIt is measured in volts (V). 2  ` Tn ??@,$  0 The  short side or  terminal of a battery is called the cathode. 8F 2f30  ` RA1 0 <$@ 0 n  ` \Asource  <$D  0 nH ` 0޽h ? 3f3fff̙3ff̙}___PPT10]+R&"D' = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(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<*`%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* `%(D' =-6B+checkerboard(across)*<3<* `DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-6B+checkerboard(across)*<3<*`D' =%(D<' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* `%(D' =-6B+checkerboard(across)*<3<* `DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* `%(+P+0+`n ++0+`n ++0+`n ++0+`n ++0+`n ++0+ `n +X  pd^(  d d C .Ahpipecir1-2"` ,$@ 0~ d s *Tn@  n  d fA- pipe1"` e <$D 0  d fAE pipe3"` H <$D 0 n d TԲn ??p@ > 2 N d Tn ??0 ,$ 0 LVoltage can be compared to the pressure of water in a tank. As the height of water in a tank increases, so does the water pressure. This increase in pressure causes more water to flow out of an opening in the bottom of a tank, much like how a higher voltage (higher electrical pressure) produces more current through a resistance..M 2L% d T(n ??@  : PContinued&   2 f3  d fAZ pipe2"`` }P x<$D 0 n  d Tn ??  ,$ 0 99 V 2  d THn ??  ,$ 0 N3 &!, 2%B  d # lZD|??@ P ,$@  0  d Tn ?? 00 ,$  0 93 A 2 d T+B#style.visibility<*d%(D' =%(D' =%(D' =4@BBBB%())))?D' =1:Bvisible*o3>+B#style.visibility<*d%(Dc' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B+checkerboard(across)*<3<*dDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-6B+checkerboard(across)*<3<* dDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-6B+checkerboard(across)*<3<* dD' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-o6Bwipe(up)*<3<* dDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-s6Bwipe(left)*<3<* dD' =%(D ' =%(D' =4@BBBB%(D' =1:Bhidden*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%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* d%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* d%(D' =4@BBBB%())))?D' =1:Bvisible*o3>+B#style.visibility<*d%(D_' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B+checkerboard(across)*<3<*dDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B+checkerboard(across)*<3<*dDT' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-6B'checkerboard(down)*<3<* dD' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-o6Bwipe(up)*<3<*dDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-s6Bwipe(left)*<3<*dDy' =%(D ' =%(D' =4@BBBB%(D' =1:Bhidden*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%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*d%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*d%(D' =%(D' =4@BBBB%())))?D' =1:Bvisible*o3>+B#style.visibility<* d%(Dc' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B+checkerboard(across)*<3<*dDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B+checkerboard(across)*<3<*dDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-6B+checkerboard(across)*<3<* dD' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-o6Bwipe(up)*<3<*dDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-s6Bwipe(left)*<3<*d++0+dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+ dn ++0+dn ++0+dn ++0+dn ++0+dn ++0+dn ++0+dn +x  ..hQ.(  hz h T, ??@P,$( 0 Here we get -9.15 V, since the red lead is hooked to the negative terminal of the battery and the black is connected to the positive terminal. 2 h bA[addition1O <$@ 0 x h c $T@    h T\  ??`@ ,$ 0 FVoltage polarity is denoted by a + and  symbol. When connecting the positive (red) lead of a multimeter to the positive terminal of the battery with the negative (black) lead to the negative terminal of the battery, a positive value of voltage will be displayed. However, if you were to connect the red lead to the negative terminal and the black lead to the positive terminal, a negative voltage would be displayed.T 2Ps_ ;6 h T  ??p @ ,$ 0 ~FLet s look at the following source:$ 2$ h Tt ??0 ` `P  B 2  h T??"` ` ,$@  0 >   h T  ??)   ,$ 0 B9.15 V  2  h N??"` 0  ,$@  0  h TX$ ??P J ,$  0 PDigital Multimeter"(22  h T??"`@ @ ,$@  02  h T??"`@ ` ,$@  0 h Tt) ?? @ ,$ 0 =+  2 h T|- ??  ,$ 0 ;- 2 h T0 ??0 pP ,$ 0 ?9.15V(2Z h Tp4 ??p@,$ 0 jNow let s see what happens when polarity is reversed.6 26 h Td8 ??0 @P ,$$ 0 A-9.15 V(2 h  j0e0e BHCpDELF$@ )8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@DH@xpXHHpppP H@ l(P@      S"  ,$@ 0 h  0e0e B C DEpF0@ )8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? 0  `         H   H  X @(  @@ @         S" p ,$@" 0 h  J0e0e BpCDE4F@ )8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? @ph(08`x @    S" p @h ,$@# 0 h  j0e0e B CDELF$@ )8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?  H   P0 p`p@PP`8 L`@      S"  @,$@ 0 h TX= ??p ,$ 0 5+ 2 h T> ?? 0 ,$ 0 5- 2 h T4E ?? p @ ,$ 0 DVo& 2  h THI ??m,$ 0 e Vo = 9.15 V> 2    h TN ?? ,$% 0 5- 2 h T\R ?? p 0 ,$& 0 5+ 2 h TX@ ??m,$' 0 f Vo = -9.15 V> 2   y h T[ ??@,$D 0 Here we get 9.15 V, since the red lead is hooked to the positive terminal of the battery and the black is connected to the negative terminal. 2U h T` ?? ,$ 0 EThe multimeter is essentially an open circuit when measuring voltage.F 2F 8H h 0޽h ? 3f3fff̙3ff̙_jWj___PPT107j.&nv+D#d' = @B Dc' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =%(D~' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =-6B+checkerboard(across)*<3<* hDK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-6B+checkerboard(across)*<3<*hD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D0' =%(D0' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* hD' =-g6B fade*<3<* hDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* hD' =-g6B fade*<3<* hDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* hD' =-g6B fade*<3<* hDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* hD' =-g6B fade*<3<* hDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =%(Dx' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*h%(D' =%(D3' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+ h ++0+ h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h ++0+h +-  {sl (  l l fAlvoltagerep1x <$@ 0 x l c $D@    l dAFvoltagerepp ` <$@ 0  l TT ??`@@,$ 0 X There are two basic ways that we can represent voltage polarity. The first is a plus/minus representation (shown on the left) and the second is an arrow. Each of these representations show equivalent polarities. In the example below we are showing the voltage polarity across a resistor.! 2! l T ??  ,$ 0 @10 V  2 l TL ?? ,$ 0 @10 V  2 l Tແ ??9 ` ,$ 0 =+  2  l T ??\ @C ,$ 0 9- 2  l T0Á ?? ` ,$  0 @10 V  2  l TƁ ?? @ ,$  0 @10 V  2/  l Z0ʁ o??"` ,$D  0 c)The arrow-head denotes the positive side.*(2*  l  0e0e B@CPDE F@ |8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@P@@"`` 0 ,$D   0 l T|΁ ??@  : LContinued&  2 f3H l 0޽h ? 3f3fff̙3ff̙___PPT10."u` +|rD' = @B Dx' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B+checkerboard(across)*<3<*lDK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B+checkerboard(across)*<3<*lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B+checkerboard(across)*<3<*lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B+checkerboard(across)*<3<*lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-6B+checkerboard(across)*<3<*lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-6B+checkerboard(across)*<3<* lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-6B+checkerboard(across)*<3<* lDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-6B+checkerboard(across)*<3<* lD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-s6Bwipe(down)*<3<* l++0+l ++0+l ++0+l ++0+l ++0+ l ++0+ l ++0+ l ++0+ l +9  P^H^;;p](  p p bAaddition2.`<$@ 0  p T ?? 0 ,$ 0 HVo* 2 ~ p s *@   5 p Tt ??n@p,$ 0 }-When appearing in series, multiple voltage sources can be added to or subtracted from one another depending on their terminal connections. In the following example we will be working with two batteries which have additive polarities, meaning that with respect to ground both batteries have the same terminal configurations. In regards to the following example this means that the positive terminal of one battery is connected to the negative terminal of the other battery, giving (from ground) a negative to positive, negative to positive configuration. 4. 2y p T  ??   > 2  p T??"` `  ,$@  0 >  p N??"` p ,$@  0  p T ??@ : ,$  0 PDigital Multimeter"(22  p T??"`0 p ,$@  02  p T??"`0  ,$@ 0  p Th ??  ,$ 0 =+  2  p T ??  ,$ 0 ;- 2 p T4 ?? P 0@ ,$ 0 ?8.80V(2 p T ?? @P ,$ 0 B9.08 V  2 p Tp ??i @PP ,$ 0 B8.80 V  2 p Tt ?? @  > 2  p Tp" ?? P `@ ,$! 0 ?9.08V(2 p Tx& ?? 0@ ,$- 0 @17.88V(2 p Tl* ?? @ ,$E 0 @-8.80V(2 p T. ?? P 0@ ,$Q 0 @-9.08V(2 p T(0 ?? P 0@ ,$_ 0 A-17.88V(2 p  J0e0e B CDE4F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? l X  @    P@| @    S" p (,$@ 0 p  Z0e0e BChDE@F @ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?t8Ph@@p0  @     S" `  ,$@ 0 p  Z0e0e BCDE@F @ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?P@P`p @     S"  ,$@C 0 p  Z0e0e B C8DE@F @ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? 0 h 0x  h 8(PHp8 @     S"  ,$@ 0  p  0e0e BC(DEdF,@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? P   @ 0 ( P @p@P ` 0x P 0H h4@        S" @h,$@S 0  p  0e0e B ChDEdF,@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?  @8h@` HXPh`0Xp(08L`@        S" p ,$@  0 p T6 ??0 P ,$  0 HV1* 2  p T; ??  ,$ 0 HV2* 2  p T@ ??@  ` ,$ 0 5+ 2  p TtC ??P Pp,$ 0 5- 2 !p TTG ?? ,$" 0 5+ 2 "p TJ ?? P ,$# 0 5- 2# #p T= ??`,$ 0 k V1 = 8.80 VD 2   L $p T8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? 8 @hx`@0X00@       S"  ,$@. 0 (p  Z0e0e BCDE@F @ )8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?hxH `pX@(H\ @     S"  ,$@/ 0$ )p Tf ??p@,$6 0 l Vo = 17.88 VD 2    *p TPm ??@ : 2  +p Tlp ??`@,$7 0 <Notice that the black lead is connected to the negative terminal of the 8.80 V source, and the red lead is connected to the positive terminal of the 9.08 V source. This allows us to find Vo by the following equation due to the - to +, - to + terminal connections. Therefore: Vo = V1 + V2 = 8.80 V + 9.08 V = 17.88 V= 2_[ W    ,p T} ?? ,$0 0 5+ 2 -p T ??P p,$1 0 5- 2 .p T ??P p,$F 0 5+ 2 /p T$ ??@ ` ,$G 0 5- 2W 0p T ??@p,$H 0 ANote: With this polarity of voltage, the value for V1 is -8.80 V.BB 24  $ 1p T< ??`,$I 0 l V1 = -8.80 VD 2    2p T ??p ,$R 0 5- 2$ 3p T ??`,$V 0 l V2 = -9.08 VD 2   W 4p Tܡ ??@@,$W 0 ANote: With this polarity of voltage, the value for V2 is -9.08 V.BB 24   5p T ??P p ,$U 0 5+ 2 6p  0e0e B CpDEpF0@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?0( H X h p@ (  `   p @ 0  8HXxpLD@         S" (,$@b 0 7p  :0e0e BCXDE(F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? x`P(@X @   S" ` ,$@a 0% 8p T  ??p,$h 0 m Vo = -17.88 VD 2    9p T ??2@,$i 0 AyNotice that the black lead is connected to the positive terminal of the 9.08 V source, and the red lead is connected to the negative terminal of the 8.80 V source. We can find Vo by adding these sources in series, realizing that the configuration sums two negative voltages (remember the - to +, - to + relationship). Therefore: Vo = V1 + V2 = (-8.80 V) + (-9.08 V) = -17.88 Vz_P    $ :p TP ??p ,$c 0 5- 2 ;p TĄ ??P ` p,$d 0 5+ 2H p 0޽h ? 3f3fff̙3ff̙___PPT10. ou z+JfD' = @B Do' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D?' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D ' =%(D. ' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B+checkerboard(across)*<3<*pDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B+checkerboard(across)*<3<*pDK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B+checkerboard(across)*<3<*pD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D&' =%(D&' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =-g6B fade*<3<*pDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =-g6B fade*<3<*pDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* pD' =-g6B fade*<3<* pDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* pD' =-g6B fade*<3<* pDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* pD' =-g6B fade*<3<* pDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* pD' =-g6B fade*<3<* pDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* pD' =-g6B fade*<3<* pD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$p%(D ' =%(DW ' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*#p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*$p%(D' =%(D3' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&p%(D' =%(D)' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*!p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*"p%(D' =%(D~' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*&p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+p%(D ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*'p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*(p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*,p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*-p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*)p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*!p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*+p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*"p%(D' =%(D3' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1p%(D ' =%(DW ' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*.p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*/p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*0p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*1p%(D' =%(D3' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4p%(D ' =%(DW ' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*2p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*3p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4p%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*5p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7p%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5p%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9p%(++0+p ++0+p ++0+p ++0+p ++0+ p ++0+ p ++0+ p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+p ++0+ p ++0+ p ++0+ p ++0+ p ++0+!p ++0+!p ++0+!p ++0+!p ++0+"p ++0+"p ++0+"p ++0+"p ++0+#p ++0+#p ++0+$p ++0+$p ++0+%p ++0+%p ++0+&p ++0+&p ++0+)p ++0+)p ++0++p ++0++p ++0+,p ++0+,p ++0+-p ++0+-p ++0+.p ++0+.p ++0+.p ++0+/p ++0+/p ++0+/p ++0+0p ++0+0p ++0+1p ++0+1p ++0+2p ++0+2p ++0+2p ++0+3p ++0+3p ++0+4p ++0+4p ++0+5p ++0+5p ++0+5p ++0+8p ++0+9p ++0+:p ++0+;p +}R  bb==t8b(  t t bAaddition3PP<$@ 0 x t c $h@    t Ti ??@  : PContinued&   2 f3 t To ?? @@ > 2  t Tq ??Z@  ,$ 0 Now, with a slightly different configuration of batteries we see what happens when the polarities oppose one another. When two voltage sources oppose each other it means that their terminal connections are opposite with respect to ground. In our next example we have a negative to positive configuration with respect to ground connected to a positive to negative configuration. With voltage polarities in this manner, the sources will work to cancel each other out.  2 t Tu ??yp` ,$ 0 B8.85 V  2 t Tl} ??y p` ,$@ 0 B9.15 V  2  t T w??"` p ,$@  0 >   t N??"` @ ,$@  0  t T ??P J ,$  0 PDigital Multimeter"(22  t T??"`@ P ,$@  02  t T??"`@ p ,$@ 0 t T$ ?? P ,$ 0 =+  2 t T, ??  ,$ 0 ;- 2 t T ??0  P ,$ 0 > 2   t  0e0e B CDEdF,@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?   (0 hh@x(pPh800(88HXh@        S"   ` ,$D 0 t  J0e0e B` CDE4F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? ` < p  `8p(X, @    S"  0 ,$@F 0, t  0e0e BCDE|F4@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@ H P pp    h p  PxHp XH h P 8x @<h@          S"  ,$DU 0 t  j0e0e B` CDELF$@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@ hP `   P ` @PX@8H @      S"  ,$D! 0 t  :0e0e B@ C8DE(F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? @  8 @ @   S"   ,$@ 0 t TH ??0  P ,$ 0 ?9.15V(2 t T ??0  P ,$@" 0 @-8.85V(2 t T$ ??0 `P ,$@0 0 >0.3V(2 t T ??0 0P ,$@H 0 @-9.15V(2 t T$ ??0 P ,$@V 0 ?8.85V(2 t T ??0 `P ,$@d 0 ?-0.3V(2 t T$ ??0 `@P ,$ 0 5- 2 t T ?? 0  ,$ 0 5+ 2 t T$ ?? `0 ,$ 0 HV1* 2   t  0e0e B CPDEdF,@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?  L ` ( @@@@P p@xp @Xp(x``HL$@        S" ( ,$@  0M  t T ??@P,$ 0 ANote: With this polarity of voltage, the value for V1 is 9.15 V.8B 25  # !t T\ ??@,$ 0 k V1 = 9.15 VD 2    "t T‡ ??0 `P ,$# 0 5- 2 #t TƇ ??@`` ,$ 0 HV2* 2  $t Tʇ ??P0p,$$ 0 5+ 2X %t T ??@P,$@% 0 BNote: With this polarity of voltage, the value for V2 is -8.85 V.BC 25  # &t T Շ ??@,$& 0 k V2 = -8.85VD 2    't  Z0e0e BH CxDE@F @ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?0 < |H 0 P   @h0p`xh@\ @     S"  p,$@. 0 (t  z0e0e BCPDEXF(@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?TP  H`HH0Pph@PXp8H$@       S" xp ,$D/ 0 )t Tڇ ??0 @` P ,$1 0 5- 2 *t TT܇ ??  ,$  0 HVo* 2  +t T@ ??P@` p,$2 0 5+ 2^ ,t T ??0@u,$7 0 For this opposing configuration of V1 and V2 (remember the  to +, + to  relationship with respect to ground discussed earlier), we find the value of Vo by the following equation: Vo = V1 + V2 = 9.15 V + (-8.85 V) = 0.3 V 2$  k    " -t T ??@,$8 0 j Vo = 0.3 VD 2    .t Td ??0 `PP ,$I 0 5+ 2 /t T ?? `P ,$J 0 5- 2N 0t T  ??@P,$K 0 BNote: With this polarity of voltage, the value for V1 is -9.15 V.8C 25  $ 1t T8  ??@,$L 0 l V1 = -9.15 VD 2    2t T  ??0 0P ,$W 0 5+ 2 3t T ?? ` @,$X 0 5- 2W 4t T ??@P,$Y 0 ANote: With this polarity of voltage, the value for V2 is 8.85 V.BB 25  # 5t Th ??@,$Z 0 k V2 = 8.85 VD 2    6t  :0e0e BCDE(F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? XPL @   S" p p  ,$@b 0 7t  0e0e B CDEpF0@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?0 0 0 ` @  P  x  ( H ` x 8 p` @  `0 (@ ` `@ `@ p`P(@         S" p @ ,$Dc 0 8t T! ??0  P ,$e 0 5+ 2 9t TH& ?? @0 @,$f 0 1- 28 :t T4) ??1@P,$k 0 For polarity of the leads switched and remembering the  to +, + to  relationship with respect to ground discussed earlier, Vo can be found using the following equation. Vo = V1 + V2 = (-9.15 V) + 8.85 V = -0.3 V~ ,   # ;t TH7 ??@,$l 0 k Vo = -0.3 VD 2    +B#style.visibility<*t%(Dh' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D! ' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-6B+checkerboard(across)*<3<*tDK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-6B+checkerboard(across)*<3<*tDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-6B+checkerboard(across)*<3<*tD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**t%(Dx.' =%(DC#' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* tD' =-g6B fade*<3<* tDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* tD' =-g6B fade*<3<* tDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* tD' =-g6B fade*<3<* tDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* tD' =-g6B fade*<3<* tDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* tD' =-g6B fade*<3<* tDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*tD' =-g6B fade*<3<*tDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*tD' =-g6B fade*<3<*tD' =K@BB5BBPB0B%(/%(@D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*tD' =-g6B fade*<3<*tD2' =%(Di' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tDi' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!t%(D ' =%(DW ' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*!t%(Dp ' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tDi' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$t%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%tC%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&t%(D ' =%(DJ ' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*"t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*$t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%tC%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*&t%(D' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'t%(D' =-u6Bwipe(right)*<3<*'tD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(t%(D' =-u6Bwipe(right)*<3<*(tDr ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"t%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-t%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*'t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*+B#style.visibility<*(t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*)t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*+t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*,t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*-t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*$t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*"t%(D ' =%(D2' =%(Di' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tDi' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/t%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1t%(D ' =%(DW ' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*.t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*/t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*0t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*1t%(D ' =%(D2' =%(Di' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tDi' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-u6Bwipe(right)*<3<*tD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3t%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5t%(D ' =%(DW ' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*2t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*3t%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*5t%(D' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6t%(D' =-u6Bwipe(right)*<3<*6tD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7t%(D' =-u6Bwipe(right)*<3<*7tDr ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.t%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:t%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;t%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*=t%(+0+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 ++0+"t ++0+"t ++0+"t ++0+"t ++0+#t ++0+$t ++0+$t ++0+$t ++0+$t ++0+%t ++0+&t ++0+&t ++0+)t ++0+)t ++0+*t ++0++t ++0++t ++0+,t ++0+,t ++0+-t ++0+-t ++0+.t ++0+.t ++0+.t ++0+/t ++0+/t ++0+/t ++0+0t ++0+0t ++0+1t ++0+1t ++0+2t ++0+2t ++0+2t ++0+3t ++0+3t ++0+3t ++0+4t ++0+4t ++0+5t ++0+5t ++0+8t ++0+9t ++0+:t ++0+;t ++0+ 2 \  x T0 ??@,$ 0 lLet s look at an example with more than two batteries:7 27  x T ??,$ 0 ?10V  2  x TH ?? ,$ 0 ?10V  2  x T ??  ,$ 0 ?10V  2  x T$ ??) ,$ 0 ?10V  2  x T  ??@,$ 0 RV14 2  x T ?? ,$ 0 RV24 2  x T ?? @ ,$  0 RV34 2  x T ??) P,$  0 RV44 23 x T ??0 6,$  0 {CFor simplicity, we will assume that all the batteries are 10 volts.D 2D  x T! ??i  ,$  0 TVout4 2 x T& ?? P  ,$ 0 )Vout = V1 + V2 + V3 + V4* 2         x TX2 ??@ `  B 2 ? x T|4 ?? ` 0 ,$$  0  Vout = 30 VF  2   B x  fDԔ?? P P ,$D  0B x  fDԔ??  ,$D  0B x  fDԔ?? 00 ,$D   0B x  fDԔ??  ,$D"  0 x T< ?? 0 p ,$ 0 :10 V 2 x Tx= ?? p ,$ 0 :10 V 2 x TC ??   ,$! 0 ;-10 V 2 x TxG ??  ,$# 0 :10 V 2 x TJ ?? . ,$ 0 Since V1, V2, and V4 all have polarities matching those of their corresponding voltage sources, the values for V1, V2, and V4 are 10 V. This concept was shown previously with the digital multimeter. 2   \   K 2  x  ` |??"` p ,$D  0 !x T$^ ??` 0 ,$D 0 Since the polarity of V3 is opposite of the 10 V source, the value for V3 is -10 V. Since we now know the values for V1, V2, V3, and V4 we can calculate the value of Vout.  2 0  "       "x Thk ??PP,$% 0 _Note: We can add V1, V2, and V4 due to their direction. However, the difference in direction in V3 means that its value must be subtracted. 2C*H x 0޽h ? 3f3fff̙3ff̙_____PPT10_.>u@*C+0DZ' = @B D@Z' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-6B+checkerboard(across)*<3<* xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-6B+checkerboard(across)*<3<* xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-6B+checkerboard(across)*<3<* xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-6B+checkerboard(across)*<3<* xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B+checkerboard(across)*<3<*xDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =%(D~' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* x%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*x%(D ' =%(DK ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*xD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*xD' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*x%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*x%(Dv' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* xD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* xD' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!xT%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!xU%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwipe(up)*<3<*xD' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwheel(4)*<3<*xD' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwipe(up)*<3<*xD' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwheel(4)*<3<*xD' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwipe(up)*<3<*xD' =%( D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwheel(4)*<3<*xD' =%( D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwipe(up)*<3<*xD' =%( D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwheel(4)*<3<*xD' =%(Dp' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bwipe(up)*<3<*xD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"x%(++0+ x ++0+ x ++0+ x ++0+ x ++0+ x ++0+ x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+x ++0+"x ++  |_(  |x | c $֋@    | jAsource2"` <$@ 0 e | T ??t@ F,$ 0 Current is the movement of electrons through a conductor, which is the time derivative of charge (dq/dt). It is established by a potential difference (or voltage) across a resistance and is measured in the quantity amperes or amps (A). 2"bB 0B 0 | T ??@P ,$ 0 d,The common DC current source is shown below:- 2-  | T ??0 pP ,$ 0 U(Independent Current Sources) 2 | ^A source2 <$D 0 C | T̹ ?? @`,$ 0 UThe arrow of the independent current source represents the direction of current flow.V 2VH | 0޽h ? 3f3fff̙3ff̙___PPT10.&np)Wa+V#DD' = @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' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B+checkerboard(across)*<3<*|D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B+checkerboard(across)*<3<*|DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(++0+| ++0+| ++0+| ++0+| +8  55%%5(  x  c $$@    0 # 0e0eA! r ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?"` H r $@ 0 D  T& ??@,$ 0 TCurrent is not across two points as is voltage, but flows through a circuit element.U 2U:  TH+ ??@,$ 0 JLet s consider the following circuit:& 2&  T/??"` P ,$@  0 >   N??"`  ,$@  0  T3 ??` Z ,$  0 PDigital Multimeter"(22   T??"`P 0 ,$@  02   T??"`P P ,$@ 0   T7 ?? 0 ,$ 0 =+  2   T; ??  ,$ 0 ;- 2   Th? ??@ ` ,$ 0 > 2  0 # 0e0eA" s ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?"` H s $@ 0   TC ??0 P  > 2 *   fF ?? P ,$ 0 `9 mA>   f@K ??P37,$ 0 t1 k2'  THP ?? p ,$ 0 b9 mA  2(  T\T ??@ @' ,$  0 p1 k(   B0e0e BCDE,F@ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? h7cf5 @   "` ` ,$@ 0   R0e0e BCDE8F @ >8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E? 0J[Ux www @    "` p,$D 0  TZ ??@P ` ,$ 0 `9 mA(2"  TI ??@P ,$ 0 j2Click to see what happens when leads are switched.3 23  Ta ??@ ` ,$D, 0 a-9 mA(2