Formule Izmjenicne_RLC Serijski i Paralelni

Frekvencija f [Hz]

f =

Kružna frekvencija ω

ω =

Efektivna vrijednost U

U =

1 T

1 [ Hz ] =  

s

2 ⋅ π ⋅ f =

U m

2

2 ⋅ π T

= 0,707U m

i (t ) = I max ⋅ sin(α ) Trenutna vrijednost u

i (t ) = I max ⋅ sin(ω t )

ui (t ) = U i max ⋅ sin(ω t + ϕ )

i (t ) = I max ⋅ sin(2π ft ) i (t ) = I max ⋅ sin(ω t ± ϕ ) Trenutna vrijednost i

I = I ef =

I max

2

u (t ) U m = ⋅ sin ω t = I m ⋅ sin ω t R R u U U m R = = = i I I m

i (t ) = Djelatni (aktivni) otpor u izmjeničnom strujnom krugu

i (t ) =

u (t )

U m

⋅ sin ω t = I m ⋅ sin ω t X L u U U m Induktivni otpor u izmjeničnom strujnom krugu X L = ω L = = = i I I m V   X L = ω ⋅ L = 2 ⋅ π ⋅ f ⋅ L  Hz ⋅ H = = Ω  A  

i (t ) = Kapacitivni otpor u izmjeničnom strujnom krugu

Serijski RL spoj

U R = I ⋅ R = U ⋅ cos ϕ 2

U = U R + U L I =

U

2

X C =

X L

u (t ) X C 1

=

=

U m X C

⋅ sin ω t = I m ⋅ sin ω t

V  1  = = Ω   ω ⋅ C 2 ⋅ π ⋅ f ⋅ C  Hz ⋅ F A

1

=

U L = I ⋅ L = I ⋅ X L = U ⋅ sin ϕ

Z = R 2 + X L

cos ϕ =

U R U

=

2

R Z

ϕ =

arctg

U L U

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U R = I ⋅ R

Serijski RC spoj

U C = I ⋅

2

2

ω C

= I ⋅ X C 2

2

U = U R + U C I =

1

Z = R + X C

U

cos ϕ =

Z

U R U

=

R

ϕ =

arctg

Z

U C U R

Serijski RLC spoj

2

2

2

U = U R + U X = U R + (U L − U C )

U R

cos ϕ =

Pojava rezonancije

X L = X C

2

2

U

2

2

Z = R + X = R + ( X L − X C ) =

R

ϕ =

Z

U L = U C

arctg

U L − U C U R

U = U R

X L = X C Z = R

cos ϕ = 1 S = P f =

Rezonantna frekvencija

1 2π LC

= f 0 = f r

R = Paralelni RL spoj

r

Ι R =

r

U R

Ι L =

U ω L

=

U

G=

X L

U

X L =

Ι R

1 R

=

I R U

B L =

U Ι L

1 X L

r

I = I R + I L 2

I 2 = I R + I L

2

Y =

2

G + B L

2

U =

I Y

= I ⋅ Z

I

G

Z

=

I L U

2



r

r

r

I = I R + I C 2

2

G 2 + BC

Y =

2

U =

2

I = I R + I C 2

I = I R + I

r

U U = 1 X C ω C

Ι C =

R

r

r

Ι L =

I X = I C − I L

I = I R + ( I C − I L ) 2

2

B X = BC − B L

I = I R + ( I C − I L ) 2

2

2

I = I R + I X Y =

=

G

U ω L

=

=

Z R

U X L

r

I = I R + I C + I L 2

I R

I Y I C ϕ Y = arctg I R

Paralelni RLC spoj

Ι R =

Y

= I ⋅ Z

cos ϕ Y =

2 C

U

I

U =

I Y

= I ⋅ Z

cos ϕ Y =

I R

=

G

I Y I X ϕ Y = arctg I R

2

G 2 + ( BC − B L ) = 2

=

Z R

G 2 + B X 2

Posebni slučaj, događa se kada se ispuni uvjet rezonancije r

r

B L = BC I L = I C B L = BC

Y = G

IX = 0

I = IR

B X = 0 ϕ Y = ϕ = 0 cos ϕ = cos ϕ Y = 1 S = P

Quk = 0



SNAGA U SLOŽENOM KRUGU izmjeni čne struje PUK = ∑ P Q L UK = ∑ Q L Q C UK = ∑ Q C Q UK = ∑ Q L − ∑ Q C SUK

PUK 2 + Q UK 2

=

cos ϕ UK

=

PUK SUK

Poboljšanje faktora snage dodavanjem radne snage ∆P =

 1

Q

−

 tan ϕ 2

1  

tan ϕ 1 

Kompenzacija jalove snage kondenzatorom

Q L = P ⋅ tan ϕ 1 Q = Q L − QC

∆

=

P ⋅ tan ϕ 2

QC = P ⋅ (tan ϕ 1 − tan ϕ 2 ) ∆S = S1 − S2 =

P cos ϕ 1

UC2 QC = U C ⋅ I C = XC C=

−

=

P cos ϕ 2

U C 2 ⋅ ω C

QC U C 2 ⋅ ω

C ≈ 66 ⋅ QC

Rad izmjenične struje W = P⋅ t Snaga u kompleksnom obliku r

r

r

S = U ⋅ I* r

r

*

r

S = U ⋅ I

= UI

cosϕ + jUI sin ϕ

r

S = U∠α U ⋅ I∠ − α I

=

UI∠α U − α I = UI∠ϕ

r

S = P + jQ

Rezonancija ili potpuna kompenzacija : uvjet je

Im(Z)=0 ili Im(Y)=0 !!!

Formule Izmjenicne_RLC Serijski i Paralelni

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