ENG04030 ANLISE DE CIRCUITOS I SHaffner Verso: 23/4/2010 Pgina 1 de 1

Expresses elementares Grandezas fundamentais ( )

( )dq ti t

dt= ( ) ( )dW tv t

dq= ( ) ( ) ( )dW dW dqp t v t i t

dt dq dt= = =

Bipolos

Conveno passiva

1

2

( )i t

( )v t+

Conveno ativa

1

2

( )i t

( )v t+

Resistor

( ) ( )tRitv = ( ) ( )tvR

ti1= ( ) ( ) ( )0

0 WdptW

t+= ( )i t

R( )v t+

( ) ( )1v t i tG

= ( ) ( )i t Gv t= 1

GR

=

Indutor

( ) ( )tLit = ( ) ( )tL

ti = 1

( ) ( )tdt

dtv = ( ) ( ) ( )0

0 +=

tdvt

( )i t

L( )v t+

( ) ( )tidt

dLtv = ( ) ( ) ( )01

0 idv

Lti

t+= ( )

( )

=

2

2 tiLtWL

Capacitor

( ) ( )tCvtq = ( ) ( )tqC

tv1=

( ) ( )tqdt

dti = ( ) ( ) ( )0

0 qditq

t+=

( )i t

C( )v t+

( ) ( )tvdt

dCti = ( ) ( ) ( )01

0 vdi

Ctv

t+= ( )

( )

=

2

2 tvCtWC

Converso tringulo-estrela Y

1R 3R

2R

BR

AR CR

1A B

A B C

R RR

R R R=

+ +

2A C

A B C

R RR

R R R=

+ +

3B C

A B C

R RR

R R R=

+ +

1 2 1 3 2 3

3

AR R R R R R

RR

+ +=

1 2 1 3 2 3

2

BR R R R R R

RR

+ +=

1 2 1 3 2 3

1

CR R R R R R

RR

+ +=

Algumas integrais indefinidas e relaes trigonomt ricas

1ax axe dx ea

= 1

lndx xx

=

11 , 11

n nx dx x n nn

+= +

( ) ( ) = axadxax sen1

cos

( ) ( )= axa

dxax cos1

sen

( ) ( )2

2cos1cos2

aa

+= ( ) ( ) 1sencos 22 =+ aa

( ) ( )2

2cos1sen2

aa

=

( ) ( ) ( ) ( ) ( )bababa sensencoscoscos =+ ( ) ( ) ( ) ( ) ( )bababa sencoscossensen +=+ ( ) ( )90sencos += aa ( ) ( )90cossen = aa ( ) ( )180coscos = aa ( ) ( )180sensen = aa