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8/19/2019 Transien AC
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TRANSIENT AC
FARIED WADJDI
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8/19/2019 Transien AC
2/25
RANGKAIAN RL
Merupakan persamaan diferensial
deraja sau idak !"m"#en$%persamaan & $% 'ers% !"m"#en (
$%Isime)a
R L V V V +=
( )φ ω +=+=
t V RI dt di
L sin0
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8/19/2019 Transien AC
3/25
• $asil 'ersamaan !"m"#en
Mis * K+ & eK
→ =+ 0 RI dt
di
L dt
L
R
I
di−=
∫ ∫ −= dt L R
I
di
K t L
R LnI +−=
K L
Rt
e I +−
=
K L
Rt
ee I .−
= L
Rt
e K I
−
= '
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8/19/2019 Transien AC
4/25
• $asil 'ersamaan idak !"m"#en
Hasil Istimewa
Hasil Istimewa
Untuk t = ~ , rangkaian mencapai stasioner
+= −
L
Rt
e K I '
( )φ ω +== t Z
V
Z
V I sin0+=
∞− L
e K I '
( )
Istimewa Hasil e K t Z V
+=+ ∞−'sin0 φ ω
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8/19/2019 Transien AC
5/25
Jika & ,- I & ,
Su.siusikan
istimewa Hasil e K I
L
Rt
+=
−
'
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8/19/2019 Transien AC
6/25
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8/19/2019 Transien AC
7/25
Arus 'erali!an
/I'0
Arus Sasi"ner
/IS0
( )( )
( )( )θ φ ω
ω θ φ
ω −+
++−
+−=
−t
L R
V e
L R
V I L
Rt
sinsin22
0
22
0
R
L ArcTg
ω θ =
( ) ( )
−+++
−+−=
−
R
L
ArcTg t L R
V
e R
L
ArcTg L R
V L
Rt ω
φ ω ω
ω
φ ω sinsin
22
0
22
0
( )φ ω φ ++−= −
t Z
V e
Z
V I L
Rt
sin.sin 00
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8/19/2019 Transien AC
8/25
1nuk & ∞I' & ,
I & I' ( ISI & IS /keadaan Sasi"ner0
( )
L
Rt
P e
R
L ArcTg
L R
V I
−
−+
−= ω
φ
ω
sin22
0
( )
−+
+=
R
Ltg Arct
L R
V I S
ω φ ω
ω sin
22
0
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8/19/2019 Transien AC
9/25
C"n"!
• Ran#kaiandisampin#
• Tenukan
a% 'ersamaan Arus
.% Teapan Waku /TC0
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8/19/2019 Transien AC
10/25
L X L .ω = Ω==
606,0100 H X X L
00
2
1!0
2===
π φ
0!",#6!060 ===
ArcTg R L ArcTg ω θ
( )( ) #
$00
22!",#60sin
60!0
200 t p e I
−−
+
−=
#
$00
01#,%#sin2
t
p e I −
−=
#
$00
#
$00
%,1",02
t t
p e X e I −−
−=−=
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8/19/2019 Transien AC
11/25
Teapan Waku
( )
( )1#,%#sin60!0
200
22
+
+
= t I s ω
( )1#,%#100sin2 += t I s
s p I I I
+=)1#,%#100sin(2%,1 #
$00
++−=
−
t e I
t
dt x R
LTC #10%,"
!0
6,0 −===
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8/19/2019 Transien AC
12/25
Ran#kaian RC
• 2ila saklar dalam Ran#kaian diuup
• 'ersamaan ran#kaian erse.u
)sin(0 φ ω +=
t V V
C
q R I t SinV +=+ .)(0
φ ω
→ → += C R
V V V
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8/19/2019 Transien AC
13/25
$asil 'ersamaan & $asil $"m"#en ( $asilIsime)a
•$asil 'ersamaan $"m"#en
Σ3 & ,
Jika kedua persamaan di deferensialkanmaka-
C
q I R −=.
dt RC I
di
I C dt
di R
dt
dq
C dt
di R
1
.1
1
−=
−=
−=
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8/19/2019 Transien AC
14/25
• Jika kedau persamaan di ine#ralkanmaka-
K t RC
LnI +−= 1
RC
t
K RC
t
K RC
t
e K
ee
e I
−
−
+−
=
==
.
.
1
&,, 1 makae K jika K =
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8/19/2019 Transien AC
15/25
'ersamaan Tidak $"m"#en
• 1nuk & ∞ ran#kaian men4apai
keadaan sasi"ner
Dimana5
)1(...1
pers Istimewa Hasil e K I
RC t
+= −
Istimewa Hasil e K I
RC +=∞−
.1
Z
t V
Z
V I
)sin(0 φ ω +==
Istimewa Hasil e K
Z
t V +=
+ ∞−')sin(0 φ ω
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8/19/2019 Transien AC
16/25
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8/19/2019 Transien AC
17/25
• 2ila disu.siusikan pada persamaan6
Arus 'erali!an
/I'0
Arus Sasi"ner
/IS0
)sin(.sin 000
φ ω φ ++
−=
−
t Z
V
e Z
V
R
V
I RC
t
2
2 1
+=
C
R Z
ϖ
CR R
C
ϖ
ϖ θ 1
arctan
1
arctan −=−
=
)sin()sin( 000 θ φ ω θ φ
++++
−=
−t
Z
V e
Z
V
R
V I RC
t
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8/19/2019 Transien AC
18/25
1nuk & ∞- I' & ,
I & I' ( ISI & , ( I
SI & IS /Keadaan Sasi"ner0
RC
t
p e Z
V
R
V I
−+
−= )sin(00 θ φ
)sin(0 θ φ ω ++=
t Z
V I S
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8/19/2019 Transien AC
19/25
• Tenukan5
6% 'ersamaan arus
7% Teapan )aku /TC0
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8/19/2019 Transien AC
20/25
Ja)a.
• 84 & 7,Ω
• φ & 9π:; & 9;<
•
θ & ar4#/984:R0 & 9=>-=?• @ &
7>Ω
At e I t )$,6#%00sin(#$,12,1
02%0 −+= −
)sin()sin( 000 θ φ ω θ φ
++++
−=
−t
Z
V e
Z
V
R
V I RC
t
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8/19/2019 Transien AC
21/25
S"al9s"al
6% Suau ran#kaian RL seri- R &
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8/19/2019 Transien AC
22/25
Suau ran#kian RC seri- R & 6,,Ω- C &7
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8/19/2019 Transien AC
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)sin()sin( 000 θ φ ω θ φ
++++
−=
−t
Z
V e
Z
V
R
V I RC
t
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8/19/2019 Transien AC
24/25
Suau ran#kian RC seri- R & 6,,Ω- C &7
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8/19/2019 Transien AC
25/25
At e I t )$,6#%00sin(#$,12,1
02%0 −+= −
)sin()sin( 000 θ φ ω θ φ
++++
−=
−t
Z
V e
Z
V
R
V I RC
t
