Electrotehnica si masini electrice (power point 3/4)

8/13/2019 Electrotehnica si masini electrice (power point 3/4)

1/41

Circuite de curent alternativ (c.a.)

Universitatea Tehnica din Cluj-Napoca, Facultatea de Mecanica 1/34

Marimi alternative

T = perioada [s]

f = 1/T frecventa [Hz] = 2f pulsatie [rad/s]

Valoare Instantanee : i(t) = Im sin(t + )

Marime alternativa = marime variabila,a carei

valoare medie este egala cu zero

Unda dreptunghiulara Unda tringhiulara

Unda dinti de fierastrau

T T

Unda sinusoidala

amplitudine

varf-la-varf

T
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2/41

Circuite de c.a.


Marimi sinusoidale

Valoarea medie: Imed= (1/T)i(t)dt = 0

Valoarea instantanee: i(t) = 2 Isin(t + )I = valarea efectiva

2I = amplitude= 2f = pulsatie

f = frecventaT = 1/f = perioada

= faza initiala

325 V

230 V

0t

[ms]2010

u(t) = 325sin(314t)

Valoarea efectiva: I = (1/T)i2(t)dt = Im/2 = 0.707 Im
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3/41

Circuite de c.a.


Defazaj

Cei doi curenti sinusoidali sunt defazati cu = /6 (30o)Curentul i2(t) este defazat in urma curentului i1(t) cu unghiul .Curentul i1(t) este defazat inaintea curentului i2(t) cu unghiul .

Curentul i2(t) trece prin zero si are valoarea maxima dupa

curentul i1(t).

=/6

i1(t)

i2(t)

t

i1(t) = I1m sin(t + 1)

i2(t) = I2m sin(t + 2)

Defazaj

= 12
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4/41

Circuite de c.a.


Reprezentare in complex. Diagrama

fazoriala

2Asin(t + ) A = A ej (j = -1)

ej= cos+ j sin

A = A (cos+ j sin)

A = A cos+ j A sin

axa reala

A

AcosAsin

axa imaginara

u(t) = Um sin(t)i(t) = Im sin(t/6)

marime alternativ

sinusoidalamarime

complexa

1i=- /6

U

I

j

U = Uej0 = U I =Ie-j/6 = I3/2

jI1/2
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5/41

Circuite de c.a.


Operatii cu marimi sinusoidale. Adunarea

u1(t) = 2U1 sin(t + 1)u2(t) = 2U2 sin(t + 2)

u(t) = u1(t) + u2(t)

u(t) = 2U sin(t + )

U = U1+ U2Uej= U1e

j1 + U2ej2

U2= U12+U2

2+2U1U2cos(1-2)

tan = (U1sin1+ U2sin2)/(U1cos1+ U2cos2)

Ucos= U1cos1+ U2cos2Usin= U

1sin

1+ U

2sin

2

U(cos+ jsin)= U1(cos

1+

jsin1) +U2(cos2+ jsin2)
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6/41

Circuite de c.a.


Operatii cu marimi sinusoidale. Adunarea

U = 43.6 V, = 23.4

Concluzie: la adunarea a doua marimi sinusoidale, fazorul

sumei este egal cu suma fazorilor celor doua marimi.

u1(t) = 220sin(314t + /3)u2(t) = 230 sin(314t)

u(t) = u1(t) + u2(t) =

= 2U sin(314t + )U = ?, = ?
http://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.html


7/41

Circuite de c.a.


Operatii cu marimi sinusoidale. Derivarea

i(t) = 2Isin(t + ), I = Iej

di/dt = 2Icos(t + )

di/dt = 2Isin(t + + /2)

Iej(+/2)= Iej/2ej=

= Ijej =jI

I

jI

1

j

+/2

Concluzie: fazorul marimii derivate se obtine prin inmultirea

cu ja fazorului marimii sinusoidale
http://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.html


8/41

Circuite de c.a.


Operatii cu marimi sinusoidale. Integrarea

i(t) = 2Isin(t + ), I = Iej

idt = -(2I/)cos(t + )

di/dt = (2I/)sin(t + - /2)

(I/)ej(-/2)= (I/)e-j/2ej== (1/j)Iej =(1/j)I

I

I/j

1

j

-/2

Concluzie: fazorul marimii integrate se obtine prin impartirea

cu ja fazorului marimii sinusoidale
http://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.html


9/41

Circuite de c.a.


Caracterizarea dipolului pasiv

Impedanta

Z = U/I []

Defazaj= (u- i) [rad]

i(t) = 2(U/Z)sin(t + u - )

u(t) = 2100sin(314t + /3)i(t) = 22 sin(314t+ /6)Z = ?

= ?

u(t)

i(t)

u(t) = 2Usin(t + u)

i(t) = 2Isin(t + i)

~

Z,
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10/41

Circuite de c.a.



RezistentaR = Z cos[]

Reactanta

X = Z sin[]= (u- i) [rad]

Z = (R2+ X2)

tan = X/R

u(t) = 2100sin(314t + /3)i(t) = 22 sin(314t+ /6)R = ?

X = ?

u(t)

i(t)

u(t) = 2Usin(t + u)i(t) = 2Isin(t + i)

Z,

~ R, X
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11/41

Circuite de c.a.



Z = (Ueju)/(Ieji)

Z = (U/I)ej(u-i)

Z = Zej

Z = Z(cos+ j sin)Z = R + j X

Impedanta complexa

Z = U/I1

j

R

X

Z

u(t)

i(t)

u(t) = 2Usin(t + u)

i(t) = 2Isin(t + i)

Z,

R, X~

Z

u(t) = 2100sin(314t + /3)i(t) = 22 sin(314t+ /6)Z = ?
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12/41

Circuite de c.a.


Puteri in circuitele de c.a.

u(t)

i(t)

u(t) = 2Usin(t + u)

i(t) = 2Isin(t + i)

~

Puterea instantaneep(t) = u(t)i(t)

p(t) = 2UIsin(t + u)

sin(t + i)
http://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.html


13/41

Circuite de c.a.


Putere activa

P = (1/T)p(t)dt

P = UIcos[W]= u - i

Puteri in circuitele de c.a.

U = Z IP = Z I2cos

P = R I2

Putere aparenta

S = U I [VA]

U = Z I

S = Z I2

Factor de putere

kp= P/S = cos

Putere reactiva

Q = UI sin

[VAr]

U = Z I

Q = Z I2sin

Q = X I2

S = (P2+ Q2)
http://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.htmlhttp://www.indezine.com/powerpoint/backgrounds/088.html


14/41

Circuite de c.a.


Puteri in circuitele de c.a. Aplicatie

u(t) = 2100sin(314t + /3)i(t) = 22 sin(314t+ /6)P = ?, Q = ?, S = ?, S = ?

u(t)

i(t)

u(t) = 2Usin(t + u)

i(t) = 2Isin(t + i)

~

Puterea aparenta complexa

S = U I*

S = UejuIe-ji= (UI)ej(u-i)=

= Sej= UIcos+jUIsinS = P + jQ

1

j

P=UIsin

Q=UIsin

S
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15/41

Circuite de c.a.


Rezistorul ideal in circuite de c.a.

u(t)

i(t)

u(t) = 2Usin(t) (u= 0)

i(t) = u(t)/R

i(t) = 2 (U/R)sin(t)

Z = R, =0R = Z cos = RX= Z sin = 0Z = R + jX = R

U = Uej0= U

I = Iej0= U/R

Z = U/I = R R = RZ = R + jX X = 0i = u =u - i= 0
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16/41

Circuite de c.a.


Rezistorul ideal in circuite de c.a.

P = RI2> 0

Q = XI2= 0

S = ZI2 =RI2 = P (kP= 1)

IR UR
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17/41

Circuite de c.a.


Bobina ideala in circuite de c.a.

u(t) = 2Usin(t + u)

i(t) = 2Isin(t) ( i= 0)

u + e = Ri = 0 u = - e

u(t) = d/dt = Ldi/dt

u(t) = 2LIcos(t)

u(t) = 2LIsin(t + /2)

Z = L, =/2R = Z cos = 0X= Z sin = L > 0

Z = R + jX = jL

u(t)

i(t)

uL(t)

L = ct.R = 0

U = Ueju =LIej/2= jLII = Iej0= I Z = U/I = jL

Z = R + jXR = 0, X = LZ = U/I = LI/I = Lu = /2 =u - i= /2
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18/41

Circuite de c.a.


Bobina ideala in circuite de c.a.

UL

IL

P = RI2

= 0, kp= 0Q = XI2= LI2> 0

S = ZI2 =LI2IL=U/(2fL)

ZL=2fL
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19/41

Circuite de c.a.


Bobina reala in circuite de c.a.

u(t)

i(t)

uL(t)

L

R

uR(t)

u(t) = uR(t) + uL(t)

U = UR+ ULU = RI + jLI

U = (R + jL)I

Z = U/I = R + jL

Z = [R2

+ (L)2

]

= arctg(L/R) < /2

UR

ULU

I1

j

c

Unghiul de pierderi= /2

R = UR/I = Usin/I,L = U

L

/I L = Ucos/(I)P = UIcos= Uisin= arcsin(P/UI)
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20/41

Circuite de c.a.


Condensatorul ideal in circuite de c.a.

u(t)

i(t)

u(t)

u(t) = 2Usin(t) (u = 0)

i(t) = 2Isin(t+i)

i(t) = dq/dt = C du/dt

u(t) = (1/C)i(t)dt

u(t) = -(2I/C)cos(t + i)

u(t) = (2I/C)sin(t + i- /2)

U = Ueju =I/(C),i= /2, I = Ieji = Iej/2 = jIZ = U/I = 1/jC = -j/(C)=u - i= -/2, (kP= 0)

Z = U/I = 1/C, =-/2,R = Z cos = 0

X= Z sin = -1/(C) < 0

Z = 1/jC = -j/(C)
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