Formule iz Osnova Elektrotehnike (I dio) koje se mogu...
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Formule iz Osnova Elektrotehnike (I dio) koje se mogu koristiti na me duispitima 0 =8.854 · 10 -12 As Vm r = 0 F = Q 1 Q 2 4πd 2 ~ E = ~ F Q E = σ E = Q 4πr 2 ϕ A = W p Q ϕ(x)= -E · x + ϕ 0 U AB = ϕ A - ϕ B A 12 = W 1 - W 2 = QU 12 C = Q U C = S d W C = QU 2 = Q 2 2C = CU 2 2 I = Q t J = NQv J = κE = I S R = U I = 1 G R = ρ l S G = κ S l R ϑ = R 20 [1 + α(ϑ - 20 W = I 2 Rt P = UI = I 2 R = U 2 R ----------------- R uk = R 1 + R 2 + ... + R n (ser.) 1 R uk = 1 R 1 + 1 R 2 + ... 1 R n (par.) 1 C uk = 1 C 1 + 1 C 2 + ... 1 C n (ser.) C uk = C 1 + C 2 + ... + C n (par.) n iz X j =1 U iz = n R X k=1 R k · I k (petlja) U = I k. R i η naponski = R t R t + R i η strujni = R i R t + R i R 1 · R 3 = R 2 · R 4 (mosni spoj) transformacija: trokut -→ zvijezda R 1 = R 12 R 31 (R 12 + R 23 + R 31 ) R 2 = R 23 R 12 (R 12 + R 23 + R 31 ) R 3 = R 31 R 23 (R 12 + R 23 + R 31 ) transformacija: zvijezda -→ trokut R 12 = R 1 + R 2 + R 1 R 2 R 3 R 23 = R 2 + R 3 + R 2 R 3 R 1 R 31 = R 3 + R 1 + R 3 R 1 R 2 μ 0 =4π · 10 -7 Vs Am ~ F = Q( ~v × ~ B) ~ F = I ( ~ l × ~ B) | ~ F | = IlB sin(α) B = μ 0 I 2πr Φ= ~ B ~ S = BS cos(α) u i = Blv e ind = -N dΦ dt = -L di dt L = N Φ I M 12 = N 2 Φ 12 I 1 M = k p L 1 L 2 e M = -M di dt u L (t)= L di(t) dt u M (t)= M di(t) dt W L = LI 2 2 ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- I ef = I m √ 2 U ef = U m √ 2 f = 1 T ω =2πf a = b + jc = Ae jα = A 6 α b = Re{a } = A cos α c = Im = A sin α A = p b 2 + c 2 u(t)= U m sin (ωt + α) u = U m e j (ωt+α) U m = U m e jα U = Ue jα = ˙ U u(t)= Im{u } X L = ωL B L = 1 ωL X C = 1 ωC B C = ωC Z R ± j X ϕ = arctan Y ∓ j B ψ = arctan B ϕ = -ψ ----------------- Frekvencijske karakteristike: Im{Z } =0 Im{Y } =0 ω 0 = 1 √ LC serija RLC : Z (ω)= r R 2 +(ωL - 1 ωC ) 2 ϕ(ω) = arctan ωL - 1 ωC R ρ = s L C paralela RLC : Y (ω)= r ( 1 R ) 2 +(ωC - 1 ωL ) 2 ψ(ω) = arctan ωC - 1 ωL γ 1 = paralela RL i RC : ω 0 = 1 √ LC v u u t R 2 L - L C R 2 C - L C 1 R ----------------- ----------------- {a } k = Φ 12 Φ 1 2 ind = ρ R | ~ F | = sin(α) QB v 1 n X j =1 I j =0 (˘ cvor) n X j =1 j =0 U X = X I I iz l u p.h. s. U = Ed · | ~ F | = 1 μ 0 I 2 · I 1 · l 2π d Q S = Q P γ ----------------- ----------------- ----------------- ----------------- = U m cos( ωt + α) U m sin(ωt + α) + j = = G G G )] X R R = U m sin(ωt + α) U 6 α =
Transcript of Formule iz Osnova Elektrotehnike (I dio) koje se mogu...
Formule iz Osnova Elektrotehnike (I dio) koje se mogu koristiti na meduispitima
ε0 = 8.854 · 10−12 As
V m
εr =ε
ε0
F =Q1Q2
4πεd2~E =
~F
Q
E =σ
εE =
Q
4πεr2
ϕA =Wp
Q
ϕ(x) = −E · x+ ϕ0
UAB = ϕA − ϕB
A12 = W1 −W2 = QU12
C =Q
UC = ε
S
d
WC =QU
2=Q2
2C=CU2
2
I =Q
t
J = NQv J = κE =I
S
R =U
I=
1G
R = ρl
SG = κ
S
l
Rϑ = R20[1 + α(ϑ− 20
W = I2Rt
P = UI = I2R =U2
R−−−−−−−−−−−−−−−−−Ruk = R1 +R2 + . . .+Rn (ser.)
1Ruk
=1R1
+1R2
+ . . .1Rn
(par.)
1Cuk
=1C1
+1C2
+ . . .1Cn
(ser.)
Cuk = C1 + C2 + . . .+ Cn (par.)
niz∑j=1
Uiz =nR∑k=1
Rk · Ik (petlja)
U = Ik. Ri
ηnaponski =Rt
Rt +Riηstrujni =
Ri
Rt +Ri
R1 ·R3 = R2 ·R4
(mosni spoj)
transformacija: trokut −→ zvijezda
R1 =R12R31
(R12 +R23 +R31)
R2 =R23R12
(R12 +R23 +R31)
R3 =R31R23
(R12 +R23 +R31)
transformacija: zvijezda −→ trokut
R12 = R1 +R2 +R1R2
R3
R23 = R2 +R3 +R2R3
R1
R31 = R3 +R1 +R3R1
R2
µ0 = 4π · 10−7 V s
Am
~F = Q(~v × ~B)
~F = I(~l × ~B) |~F | = IlB sin(α)
B = µ0I
2πr Φ = ~B~S = BS cos(α)
ui = Blv eind = −N dΦdt
= −Ldidt
L = NΦI
M12 = N2Φ12
I1
M = k√L1L2 eM = −M di
dt
uL(t) = Ldi(t)dt
uM (t) = Mdi(t)dt
WL =LI2
2−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
Ief =Im√
2Uef =
Um√2
f =1T
ω = 2πf
a = b+ jc = Aejα = A 6 α
b = Re{a} = A cosα
c = Im = A sinα
A =√b2 + c2
u(t) = Um sin (ωt+ α)
u = Umej(ωt+α)
Um = Umejα U = Uejα = U̇
u(t) = Im{u}
XL = ωL BL =1ωL
XC =1
ωCBC = ωC
Z R ± jX ϕ = arctan( )
Y = G ∓ jB ψ = arctan(B)
ϕ = −ψ
−−−−−−−−−−−−−−−−−
Frekvencijske karakteristike:Im{Z} = 0 Im{Y } = 0
ω0 =1√LC
serija RLC:
Z(ω) =√R2 + (ωL− 1
ωC)2
ϕ(ω) = arctanωL− 1
ωC
R
ρ =
√L
C
paralela RLC:
Y (ω) =√
(1R
)2 + (ωC − 1ωL
)2
ψ(ω) = arctanωC − 1
ωL
γ1
=
paralela RL i RC:
ω0 =1√LC
√√√√R2L −
LC
R2C −
LC
1R
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
{a}
k =Φ12
Φ1
2
ind
=ρ
R
|~F | = sin(α)Q Bv
1
n∑j=1
Ij = 0 (c̆vor)
n∑j=1
j =0U
∑=
∑I I
izlu
p.h. s.
U=E d·
|~F | =1
µ0I2· I1· l
2π d
QS =QPγ
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−=Umcos(ωt+α) Umsin(ωt+α)+j
=
=GG
G
)]
XR R
=Umsin(ωt+α)
U6 α=
