Tugas Nilai Awal Syarat Batas Oleh Dwi Kurniati Zaenab

  • May 2020
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  • Words: 480
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Nama

: Dwi Kurniati Zaenab

NIM

: 105017000416

Tugas

: NASAB (Aplikasi PD pada jaringan listrik)

Soal : Suatu jaringan listrik terdiri dari sebuah induktansi 0.1 henry, tahanan 20 ohm dan suatu kondensator yang berkapasitansi 25 mikrofarad ( 1 mikrofarad = 10-6 farad). Carilah muatan q dan arus i pada saat t, jika diberikan syarat awal q = 0.05 coulomb dan i = dq/dt = 0 jika t = 0.

Jawab: Karena L = 0.1

C = 25.10-6

R = 20

E(t) = 0

d 2q dq q L 2 +R + = E (t ) dt c dt d 2q dq q 0.1 2 + 20 + =0 dt 25.10 −6 dt d 2q dq + 200 + 400000q = 0 2 dt dt d 2q  dq L  2 + 200 + 400000q  = L{ 0} dt  dt 

S 2 Q − Sq (0) − q' (0) + 200( SQ − q (0) ) + 400000Q = 0 S 2 Q − S (0.05) − 0 + 200 SQ − 10 + 400000Q = 0 S 2 Q + 200 SQ + 400000Q = 0.05S + 10

(

)

Q S 2 + 200 S + 400000 = 0.05S + 10 0.05S + 10 Q= 2 S + 200 S + 400000 0.05S + 10 Q= ( S + 100) 2 + (100 39 ) 2 0.05( S + 100) + 0.05(100 ) Q= ( S + 100) 2 + (100 39 ) 2 Q=

0.05( S + 100 )

( S + 100)

(

2

+ (100 39 )

(

2

))

+

0.05(100) 39

(( S + 100 ) + (100 39 ) 2 ) 39 2

(

 0.05 Q = e −100t 0.05 cos 100 39 t + e −100t  sin 100  39   0.05 Q = e −100t  0.05 cos 100 39 t +  sin 100 39  39 

(

{(

(

(

Q = e −100t 0.05 cos 100

)

 39 t    t  

)) ( ) 39 )t ) + (0.008 sin (100 39 )t )}

Misal: A = 0.05

B = 0.008

dq dt d −100t i= e A cos 100 39t + B sin 100 39t dt i = −100e −100t A cos 100 39t + B sin 100 39t + i=

(

{

(

) ( ( ))}) { ( ) ( )} {− 39 A sin(100 39t ) + 39B cos(100 39t )} e {( 39B − A) cos(100 39t ) − ( 39 A + B ) sin(100 i = 100e −100 t

−100 t

i = dq/dt = 0

jika t = 0

maka:

{ ( 39 ( 0.05) + 0.008) sin(100 {− 0.32 sin(100 39t )}

i = 100e −100t − i = 100e −100t

39t

)}

39t

)}

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