: ; .
1. .
( ) R , L , . :
- R, , G = 1/R, C;
- L, , XL = 2πƒL, BL = 1/XL, ;
- , , XC = 1/2 πƒC, BC = 1/XC .
.
, R, (, ). R (.1)
u = Um sinω t.
. 1.
u = Ri, . .
Im = Um/R I = U/R.
, , (. 2, .3).
φ = ju - ji = 0 - 0 = 0
:
= ej 0; φu = 0 ;
İ = Iej 0; φi = 0 .
Z = /İ = Uej 0 /Ie j 0 = R,
. . , R
( ) . 2 3.
. 2. . 3.
R- R-
, (, ). , , + 1.
:
p = ui = U msinω tIm sinω t = UmIm sin2ω t = UI (1 cos2ω t),
. . . , . cosφ = 1, .
= UI = RI 2,
, , , .
R - , . . .3.
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:
,
W = UI = RI2, , . , , , .
R = UR/I, P = PW.
.
, . , . , 1 .
, , . .
, .
. 4. -
u = U sinω t. i Q = Cuc, u - .
u = uc.
, , :
i = dQ/dt = ω CUm cosω t = ω CUm sin(ωt + π/2) = I msin(ω t + π/2),
Im = ω CU m = Um /(1/ω C).
, π/2 .
1/ω C , / = / = = / = ).
X = 1/ω C = 1/2π fC = U c/ I
.
= Uej 0; ψ u = 0º;
İ = Ie j 90; ψ i = + 90º;
φ = ψ u - ψ i = 0º - 90º = - 90º.
Z = / İ = Uej 0/ Iej 90 = e - j 90 = -jX.
, - .
:
= ui = U msinω tI msin(ω t + 90) = UI sin2ω t,
. . . , , , .
, . , , . Q, Q = UI = - XI2, Q , , , .
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- .
:
S = = Sej φ = UI cos90 - jUI sin90 = - jUI,
-, ( ) . 5,6.
I
. 5. .6.
- -
- Qc Uc I :
= Uc/ I,; Qc = Uc I .
|
, , , . . , , .
, (, ).
L, R = 0.
. 7.
u = U msinω t. i, .
L = - wd /dt = - Ldi/dt,
w - .
( ) , L , .
u, i, eL L. L , uL.
II u - uL = 0, , uL = - L,
u = eL = 0
Um sinω t Ldi/dt = 0, di/dt = Um sinω t / L.
:
i = (Um/L)sinω t d t = - Um cosω t /ω L = Um sin (ω t - π/2)/ω L =
= Im sin(ω t - π/2).
, π/2 .
ω L , / = ·/· = = .
XL = ω L = 2π fL.
. :
Im = Um/XL, I = U /XL.
, XLI = U = L
, i eL.
= Ue j 0, ψ u = 0o;
İ = Ie - j 90, ψ i = - 90o.
φ = 0 (-90) = +90o
Z = / İ = Ue j 0/ Ie - j 90 = XLej 90 = jXL.
, L - .
|
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Z = XL
L -:
= ui = Um sinω t - Imsin(ωt - 90) = - UIsin2ωt.
. . . , . , . , , . QL = UI.
QL = ULI = XLI 2, , , .
:
S = = Sej φ = UI cos90 + jUI sin90 = jUI,
( ) 8 9.
.8. .9.
.
R L (.9).
.9. R L -
Z = R + jX L = zejφ
φ = arctq XL / R
İ = / Z . .
:
= R İ; UL = jXL İ
.10.
İ
.10. ; ψi = 45º