CS作业代写 IH 10 cos 1300T Be 10ed

Any cosinusoidally time varying function xLH Acos wt 0 can be represented as

It Re Aeiht1013 The Aei0eJwt

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Time independent part i e X Aei or A201 is called the phaser counterpart

of It Then

a X IH 10 cos 1300T Be 10ed

X IOeJ0 I1

b Xslt 5cos lot 3140 5cos lot 3140 3601 5 cos lot 1460

usually the rageof the phaseangle is chosen between

180 to 1800 or IT to X

Re Sei lot 1469 Be Ses t e t X 5L

c Xslt 16sin150T 30 16cos Sot 30 900 16cos 150T 1200

Be lbe5 50T 120 3 Re If e
51200ejSot

Xg 16e Jk0 16L izo1

ECE 2020 AU22
Hw7 Solutions

For agiver angular frequency w time domain counterpart of a phaser Ae is

lH Re AeJ0eJwt A cos wt 0

where w 2Af Hence Ae A cos wt 10 For this problem

w 2Xf 271 60 1201T rad Is

a f the 32 eJ28 eJwt 32 cos wt 284 32 cos 1120kt 280

b 5120 Slew 51 hence

LH Be 51eJwt 51 cos wt 51 cos 1120kt

c 102 65 10 e Jbs hence

zlH The 10eJb e’wt locos wt 650 locos 120kt 650

d x It Re 1 e eJwt L cos Iwt t 132 cos 1120kt t 1320

a Za I 1 j 4 a
j w C j 50 10

b Z jwL j 5 103 2 10

c Za R IS r

Transfer to phaser domain

vsLt 12 cos 2500T 300 Vs 12 300 V and w 2500 radlsec

Z jWL j 2500 300 10

Zc 1 1 j 200 r
jw C j 2500 2 10

2 j7SOr Total impedance of the circuit

Zo 5200 r ZT ZL c Zc Zr

j 750 j 200 4001 til
400 j 550 r4001

ffooEssoTLtan 13 1
680.07 53.970

12_ 2300 53.970 17.66 L 23.970mA
680.07 253.970 680.07

I 200 900 17.66 10 3 L 23970 3.53 L 113970 V

veLt Be 3.53 e J
7 ed t 3 3.53 cos 2500T 113.970 V

Switch to phasor domain

vsLt 120 cos 12000T V 3 Vs 120 LO V and w 2000 rad Isee

2 L jw L j 2000 200 10

2 c j 100 R

u noon if soon

2 T 3001 Kj 3001

15052 4450 150 j 150 r x 212 13 245

1 120 00 2527 450 450 Ay 0.57
15052 450 5

a Complex power associated with the source is

S Vs Io I 120 e.JO 2 ed 120 Lo EL 45

24527 e 5450 VA

24527 cos 145 j sin 145

24 j 24 VA

the real power generated by the source is P 24W

the reactivepower of the source is Q 24 VAR

Pf 24 a 0.71 lagging

Since source current Io lags the source voltage Vs by 450 we have a

lagging pf

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