!" # $ ! " !# " $ % % & & ' S % & " # ' % & & E S I % " # % %& %# ' $ (# !" # $ ' $(# ()$% % % 1-1 ' $ (# & % ' ( = & " ) ( * % & * % ' " # + & % 1.1.2 CAMPO Y POTENCIAL ELÉCTRICO ' " # , & & , & 0 & % = %$* 0 "-./# & ( $ % +'# ( $ ! % * 1 2*1 1-2 ( = "3) /# − =− 1 * ' "4 +'# ( $ ! 5# "3) /# " 26 7# % 2" # = − ∞ , & " % # * & % 8 ! 9 + & 8 / " # & % +Q +Q -Q -Q E V V d 1-3 , & , % % % ' / % ! ! " % " # # * : ) = ) $ ( < < = ; = = ( / ; = = ' $ 8 & , % "-# ) =) ) =) ( ) 8 % % " &# "'&# .- )79> 0 (- )79? 0 +- )79)< 0 1-4 % % ) 777 0 @ * & )77 0 )77@ % ( ( + / % & 9 $ A " " *# ε7#( ε ⋅ = ' 9 + & /' & & / % B BCD)79)<0. /' 9 0 1+!' 9 ) = , / B BC ⋅ )7 −)< . = 7 77) ε7 ⋅ ) ⋅ ") # < = B BC ⋅ )7 −? = B BC = B BC 2 * & ( = ) < = ) < < = ) < < 0 1+!' 3 9 / 9 )77 7) EF & ;72G EF & 1-5 G = ε ⋅ = ⋅ = ⋅ < = "B BC ⋅ )7 −)< . # ⋅ "7 ) # < = B BC ⋅ )7 −)7 7 777) = 7 BBC = = 7 BBC = BBC ⋅ ;7 = <> CC "<> CC ⋅ )7 −? # ⋅ ;7 < = ;?B <C ,3 = : = − = +Q C1 -Q ) + +Q < C2 -Q a * b V2 V1 V Ceq * & $! +Q $" & $" V $! $! $" ' ) ) ! ' "* ( = ) + < H = ) = < = ) < ( = + ) -Q ( < 1-6 = F( ) = ) + ) ) < ) ( 0 1+!' , 9 = )< ) /) ) + ) = ) ) = >I0 /< ;I0 = ) = ) = = = ) + ) ⋅ ) = < < = ⋅ <J µ >µ < ⋅ ) + ) = < < < = > µ ⋅ ;µ >µ + ;µ = <µ = < µ ⋅ )< = <J µ =J < = = < <J µ ;µ =B / ,, & $! ! $" +Q1 " C1 -Q1 $# ' # ) ! " # +Q2 & $ +Q3 + C2 C3 -Q2 -Q3 V = ) + < + ; = ⋅ = ) ⋅ + < ⋅ + ; ⋅ Ceq +Q 1-7 -Q V = 2 = H ) + < + ; = 0 1+!' 4 9 I0 /;6 JK I0 /)6 J K I0 /<6 )7 / <J 2 / / 6 /)3/<3/; 6 J K I0 3)7 I0 3JK I0 6 >) KI0 F) 6 /)D2 6 J K I0D<J2 6 ))< B I/ F< 6 /<D2 6 )7 I0D<J2 6 <J7 I/ F; 6 /;D2 6 JK I0D<J2 6 ) )<B I/ 0 1+!' 5 9 /)6 J K I0 /<6 < < I0 <J /;6 > B I0 / = C2 /< /; Q2 C1 Q1 <; = + < = < < + > B = ?µ ; C3 V1 /) / Q3 <; V2 ) ⋅ = <; + ) <; = J K⋅? 7 = ; 7? µ JK+?7 V C1 F = = ) = ⋅ ) ) ) = = / ( = ; 7? µ ⋅ <J = KJ )> µ <; Ceq23 Q1 V1 V2 V = KJ )> µ +Q Ceq KJ )> = )C KK JK V 1-8 -Q Qeq23 < <; = = <; KJ )> = B <J ? < = < ⋅ < = < <µ ⋅ B <J = )B );µ ; = ; ⋅ < = > Bµ ⋅ B <J = C> 7;µ F <; 6 F; 3 F< 4 ' & & & ( ) ) = < = < ; = =! !6L & ; l S E I V & A & & % ' ( + I - a b R V ( ( * A 1-9 " #! + % % , 9 % , 8 & ".#( % $ La inversa de la resistencia se llama Conductancia y se designa con la letra G, siendo G = 1/R. .0! / " # 0 1+!' 6 7 0 8 < K77 M 8 JNK M & < K @M <@K M J K77 777 M J K77 @M * J K NM A / -) 1 & % "2# , ' ( != ρ⋅ % ( 2 1-10 N 2 .* < ;C7 D )79B ) C?7 D )79B ) >K; D )79B < >CC D )79B ? K)7 D )79B : ' / * $ J ;77 D )7; * )7)7 9 )7)J )7); )7B 9 )7)) 2 + N , & A / / -) , * 4 ' & I a b R V - ( ) 0 ( ( ( &! &! ' # !<DL6 2<.L #! ! 8 % 9':! "; 1-11 & & & % % O 0 1+!' < 9 ' < % )7 <7 * / !=ρ = % ") >K; ⋅ )7 −B Ω ⋅ # ⋅ ")7 # 6 ); ;<D)79;M 6 ); ;< −C < ) <C>> ⋅ )7 6 PD < 6 ; )J)>D"7 77<#< 6 ) <C>> )79C ' M < <7* 2 6 !DL 6 <7D); ;< D)79; 6 <>> JD)79; 2 6 <>> J 2 0 1+!' = 9 ' EF & KC Q <<72G EF & RQD% G E/ <J % = &! != = KC <<7 = 7 ;J = <<7 7 ;J = >JKΩ : L( < != G &! = "<<7 # < = >JCΩ KC ! ( 1-12 'L DS 6 KCQD<J% 6 7 7KCRQD<J% 6 ) B RQD% 43 & % , , ' ( ' ( I ) R1 R2 V1 V2 R3 / #! ' #!' ) #!) V I Req = #! V #! ( #!' ( #!) = ( ! ! ( !' ( !) ( ! = ! ' ( 1-13 V3 ) = !) = 0 1+!' > 9 / )< RM !) T !) + !< < = !< = !< !) + !< L) 6 < K77 M L< 6 ;R; M L; 6 )R M LJ 6 / ;B 2 L 6 < K RM 3 ; ; RM 3 ) RM 3 )< RM 6 )? 7 RM (2 62 ' ! ! ( 2) 6 ;B2 < K *Ω 6CJ2 )?*Ω 2< 6 ;B2 ; ;*Ω 6>>2 )?*Ω 2; 6 ;B2 ) 7*Ω 6<72 )?*Ω 2J 6 ;B2 )< 7*Ω 6 <J 7 2 )?*Ω ;B2 4, = & * , / ( I ( ' ( / 2 #! + R1 ) '#!'+ R2 I1 ( V I2 )#!) I 1-14 V R3 Req I3 #! = ! , ( = ! !) = + !< + !; 2 ) ) ) ) = + + ! !) !< !; = ( ) = ! ) ! ( , , ( ,' ( ,) = , , ( !) ⋅ !< !) + !< ! * ( ) = !) 0 1+!' ? 9 ' ; 7M L< 6 > 7 M !< T !) + !< = < = !< = !) !) + !< L) 6 % ! 6 >* / ; 7M 1-15 L 6 !) ⋅ !< ; 7Ω ⋅ > 7Ω 6 < 7M 6 !) + !< ; 7Ω + > 7Ω I R1 R2 I1 I2 V 2 6 !DL 6 >*D< 7M 6 )<2 !) 6 ! !< >Ω 6 J* 6 >* !) + !< ;Ω + >Ω !< 6 ! !) ;Ω 6 <* 6 >* !) + !< ;Ω + >Ω 'L) 6 !)<DL) 6 J<D; 6 JBQ 9/ 0 1+!' ;>2 L)6 ) 7 M L<6 J 7 M L;6 )< 7 M LJ6 C 7 M ' I1 - -" -# I R2 R4 R1 I2 ! = < −; !< ⋅ !; JΩ ⋅ )<Ω = = ; 7Ω !< + !; JΩ + )<Ω V *% I ! ! (! = ! ! '")(!- R1 Req2-3 R4 6 )M3;M3CM 6 ? 7M I ;> = =J ?Ω !- R3 Req V 6 J* !) !<( ) = !; )<Ω = =;7 !< + !; JΩ + )<Ω < = !< JΩ = =)7 !< + !; JΩ + )<Ω JM )< M 1-16 #! 6 J*D)M 6 J2 ! !' !) !- #!- #!' '#!) #! '") 6 J*D;M 6 )<2 - #.$ 6 <72 1.1.5 AUTOINDUCCIÓN O INDUCTANCIA L $ % % & & & 3 3 / ' & % & & 0 = φ 4 5 & i(t) / S & & 0 V % 6 6 ' , & & φ= ⋅ % & & φ) ) = φ< = ( φ =0 < 1-17 =0 * 7 6 * 0 ( =0 6 & 6 % " # )$6 )Q .)* ( ! U 8 1:1!-* 9 : -:!= 6 ' 6 8 ( φ =1⋅ 5 = 0⋅ 2 @ / & = ( = 0⋅ < < 6 & % 1-18 0 1+!' 3 9 ' < )7 * 6 ;7I$ % )77I / EF & )7*G ' ( = ∆ )7 −< = ∆ 7) = ;7 µ2 ⋅ B7 = 0⋅ 0⋅ = < < = B7 % = B7 = < J77 µ % =<J ;7 µ2 ⋅ ")7 # < = = ) C77 µ = ) C < 1-19 3- @ ' , & & & " & # & * + )$A') L ! 1 (#') / % % ! 1 (#') #$A') / " # " 3 - # @ = & $% ! # 8 & " 6 & & 3 V / 3 % I I + V + + + V Vg - Vg V Vg - I 1-20 -7 " # & ( &!0 = H &= ⋅ ⋅ &= 3 ⋅ 3 8 ' % % I I + + + + RL V Vg Circuito V Vg - - & & $$ ' -* + & - I I + + V Rg Rg V V Vg + + Vg 4 Vg - I - Icc 1-21 / % 4 - 3 3 5 & = / 9 ( 3 − ⋅ !3 % 4 ( = 3 !3 / ∞ !0 4 / ! 3 2 L ( 3 !3 = = ( &= 3 = I 3 ⋅ = < ⋅ ⋅ !3 + ⋅ − ⋅ !3 = I + 3 + ⋅ !3 + Rg Rg V V RL + + Vg Vg - - 1-22 Circuito 33= $% ! & * & & " # ( I I + Ig + V I Ig V Ig - - V / 3 & - 7% ( = !0 ⋅ = !0 ⋅ I 3 I + Ig - V RL Ig Circuito V - + &= < ⋅ !0 = ⋅ % / & = "− # ⋅ = − ⋅ * & & 2 ' 1-23 -* + & - I I + Ig I + IRg IRg Ig V Rg Ig V Rg - ∞ V - Vca !3 = !3 ( & W ( = 3 − !3 = 3 − !3 &= ⋅ ( < &3 = ⋅ 3 = !3 0 1+!' , 9 8 + ⋅ = ⋅ !3 + ⋅ JC 2 7C M J M / J C− ⋅7 C = ⋅J = 3 − ⋅ !3 = ⋅ !0 = 3 − ⋅ !3 = J C − ) ⋅ 7 C = J &3 = &!3 = &= 3 ⋅ = J C ⋅) = J C < ⋅ ! 3 = )< ⋅ 7 C = 7 C ⋅ = J ⋅) = J ' 6 ' 3 'L 1-24 =) , B -- * ' @ %% & , /!L/8!+: " W/+L!/:( # % -8=:( = N* + *( / & L*N*( / 8 ,3 H , ' ( = 6 ( ) + < + J = I2 I1 ; I3 I4 ( =7 , 0 !* 1-25 ,, / = ( I c + d =7 Rg * V ( + + + / " − + = − #+" − − =− − = ⋅ !3 − = − = ⋅ !0 =7 + Vg - a ( #+" − RL b #+" − #+" − e #=7 3 − = ⋅7 = 7 9 ( − / 3 + ⋅ !3 + 7 + ⋅ !0 + 7 = 7 3 ( 8 1-26 = ⋅ " !3 + !0 # = 3 !3 + !0 V / & % " # % R1 I V1 / Rg 0 / R2 % + ! Vg " V2 R3 a ' L ( ⋅ !; + < + "− 3 # + ⋅ !3 + ⋅ !) + "− ) # + ⋅ !< = 7 " = ! ( = 3 + ) − < !) + !< + !; + !3 % % % , ! 6 , 6 , 1-27 ( & % ,4 ( )9' % % % % <9 L ;9 L J9L & $ " & # & % 8 , : & % , 2 & 1-28 0 1+!' 4 9 2) 6 < 2 2< 6 ) 2 2; 6 ; 2 / ! " L)6 J M L<6 < M L;6 ; M 2 # % ( + & % ( $ ( ( % ; = ) + < I1 e =7= ; − ) − R3 a c < < I3 V2 R1 I2 V3 R2 ( V1 & f -! -! ! -" " b d ! " ( ) − ) ⋅ !) − < + < ⋅ !< = 7 ) − < = ) < + ; = < ⋅ !) − < ⋅ !< ( ( − ; ⋅ !; + ; / − < ⋅ !< + < =7 ⋅ !< + ; ⋅ !; % ( ; = ) + < < − ) = JD ) − <D < ) = JD ) − <D < ) + ; = <D < + ;D ; J = <D ; < + ;D = <D < + ;D" ) + L < # = ;D ) + CD ( 1-29 < ) =7C =7C < ; =) * ' ( % ( & & ( ( = )D!) − ) =− < + < D!< = − ; D!; + ; = 7 CDJ − < = −) + 7 CD< = −)D; + ; = 7 ( ( ) ( &! = < ) < D!) + < < D!< + ; D!; = 7 C< DJ + 7 C< D< + )< D; = ) + 7 C + ; = J C ( &3 = ) D )+ < D < + &! ; D ; = <D7 C + )D7 C + ;D) = ) + 7 C + ; = J C &3 1-30 4 C @ & 4 & C * ' % ( , , 8 % % % @ %% ( I ! = V 1-31 Circuito 43 C $ :$#' $ :$#' 3 $ :$#' 3 +%& -:; :; +%& +%& A Circuito 1 Circuito 2 B ' $ :$#' 3 +%& & $ :$#' ( 3 3 :; $ :$#' $ :$#' $ :$#' 3 ' @ -:; %% 3 ' $ :$#' A A RTH Circuito 1 + VTH RTH VTH B $ :$#' $ :$#' 3 = B +%& ' % $ :$#' A + RTH Circuito 2 VTH B 1-32 4, $ :$#' $ :$#' 3 $ :$#' 3 - 4 8 - -8 A Circuito 1 Circuito 2 B ' $ :$#' 3 - $ :$#' ( 3 3 8 $ :$#' ' @ %% -8 3 ' $ :$#' ? A RN RN IN Circuito 1 A IN B $ :$#' 3 B - $ :$#' % ' $ :$#' = A IN RN Circuito 2 B 1-33 44 @ % , % ' I -7 Vg Red RL V Ig pasiva IV Vg Red RL VV pasiva @ / %% & II Red RL VI Ig / @ %% pasiva & 8 ( = + = + 1-34 5 & C = 8 ( I + Rg V 1 + = 3 !1 = !3 !3 Vg - / % 8 ( 1 = 3 !3 -8 !1 = !3 Rg Rg IN RN + Vg & 3 1-35 !3 % * +%& I + IRg Ig V Rg 72 = 3 D! 3 + !72 = ! 3 - +%& :; - 72 3#!3 Ig RTH Ig Rg VTH Rg 1-36