[1]
(1-a)
−
Vout ( jw ) =
x −
x
Vs ( jw ) =
0
2d
2d
(1-b)
[2]
ZC =
1
−j
=
= − j20Ω
jC 100  500 10−6
Z L = j L = j100  0.2 = j20Ω
Applying KCL at node 1, we have:
Is =
1
V1 V1 − V2
1 
1
j 
j
 1
+
 Is =  +
 V1 − V2  400 =  + V1 − V2
R1
ZC
ZC
20
 40 20 
 R1 Z C 
Applying KCL at node 2, we have:
V1 − V2 V2 V2
V  1
V1
1
1 
1
1
1
=
+
 1 = +
+
= ( − j + j )V2
 V2  j
ZC
R2 Z L
ZC  R2 Z C Z L 
20 10 20
20
Therefore,

1 
j
 1

j 
j
 1
400 =  40 + 20  V1 − 20 V2



400 =  +  ( − j 2V2 ) − V2

20
 40 20 

V
1


j 1 =
V = − j 2V
V
 1
2
 20  10  2

j
1
j
j 
1
400 = − V2 + V2 − V2 =  −  V2

20
10
20
 10 10 
V = − j 2V
 1
2
V2 =
400
= 282.8445 V , V1 = − j 2V2 = 565.68 − 45 V
j 
1
 − 
 10 10 
 v2 (t ) = 282.84 cos(100t + 45 )V , v1 (t ) = 565.68cos(100t − 45 )V
[3]
Current I s =
Vs
230
20
=
=
= 20.18 − 15.26 A
R + Z L 1 + 10 + j 3 11.415.26
(3-a)
PLave =
VL I
cos  =>
2
VL = Vs 
P ave =
ZL
ZL
= 2300
= 210.61.44
R + ZL
R + ZL
210.6  20.18
 cos(1.44 + 15.26) = 2035.33
2
* Vrms 로 이해했을 경우 1/2를 뺀 4075.66도 해답임.
(3-b)
VR = Vs 
R
230
=
= 20.18 − 15.26
R + Z L 11 + j 3
Pave = I s VR = 20.18  20.18  cos(−15.26 + 15.26) = 20.182 = 407.23
(3-c)
Power factor = cos15.26 = 0.9647
[4]
(4-a)
Z𝑅0 ll 𝑍𝐶 = 𝑅0*(1/jwC)/{ 𝑅𝟎+(1/jwC)}
= 𝑅0/( jwC𝑅0 +1)
= 160000/(10000 + 6032j)
= 11.73 – 7.0764j (ANS) (11.1435~12.3165 – j6.72258~j7.43022 인정)
(4-b)
𝐼𝑠 = (𝑉𝑠 - 𝑉𝑙𝑜𝑎𝑑 )/ 𝑍𝑅𝒔
= (141.4∠0 – 125.4∠-0.0669)/2
= {141.4(cos(0) + jsin(0)) + (-125.4)(cos(-0.0669rad) + jsin(-0.0669rad))}/2
= {(141.4cos(0) – 125.4cos(-0.0669rad)) + j(141.4sin(0) – 125.4sin(-0.0669rad))}/2
= {141.4 – 125.12 + j8.383}/2
= 8.14 + j4.192 (ANS) (7.733~8.547 + j3.9824~j4.4016 인정)
= 9.156∠0.4758(rad) (ANS) (8.698~9.6138∠0.45201~0.4996(rad) 인정)
= 9.156∠27.26(degree) (ANS) (8.698~9.6138∠25.9~28.62(degree) 인정)
(4-c)
𝐼𝑟𝑚𝑠 = 𝐼𝑚𝑎𝑥 / √2 (∵ sinusoid)
= 9.156 / √2
= 6.473 A (ANS) (6.149~6.7966 A 인정)
(4-d)
(𝑉𝑠 - 𝑉𝑙𝑜𝑎𝑑 )/ 𝑍𝑅𝒔 = 𝑉𝑙𝑜𝑎𝑑 / (Z𝑅0 ll 𝑍𝐶 )
𝑉𝑠 / 𝑍𝑅𝒔 = 𝑉𝑙𝑜𝑎𝑑 *{1/(Z𝑅0 ll 𝑍𝐶 ) + 1/𝑍𝑅𝒔 }
= 𝑉𝑙𝑜𝑎𝑑 *{( jwC𝑅0+1)/ 𝑅0 + 1/𝑅𝒔}
= 𝑉𝑙𝑜𝑎𝑑 *[{( jwC𝑅𝒔 𝑅0 + 𝑅𝑠) + 𝑅0}/𝑅0 𝑅𝑠]
So,
𝑉𝑙𝑜𝑎𝑑 = [{(jwC𝑅𝒔𝑅0 + 𝑅𝑠 ) + 𝑅0 }/𝑅0 𝑅𝑠]−1 * 𝑉𝑠 / 𝑍𝑅𝒔
= [𝑅0 𝑅𝑠 /{(jwC𝑅𝒔 𝑅0 + 𝑅𝑠) + 𝑅0 }]* 𝑉𝑠 / 𝑍𝑅𝒔
= [ 16*2 / {( j377*100*10−6*2*16 + 2) + 16}]*141.4∠0 / 2
= 16 / (18 + j1.2064) * 141.4∠0
= 125.4∠-0.0669(rad) or 125.4∠-3.834(degree) (ANS)
(119.13~131.67∠-0.0703~-0.0636 (rad) or -4.0257~-3.6423 (degree) 인정)
(4-e)
𝑉𝑟𝑚𝑠 = 𝑉𝑚𝑎𝑥 / √2 (∵ sinusoid)
= 125.4/√2
= 88.67 V (ANS) (84.2365~93.1035V 인정)
(4-f)
𝑃𝒂𝒗𝒆 = 𝑉𝑟𝑚𝑠 * 𝐼𝑟𝑚𝑠 * cos (θv − θi)
= 88.67 * 6.473 * cos(-31.09degree)
= 491.08 W (ANS)
[5]
(5-a)
𝑉𝑜𝑢𝑡 (𝑗𝜔 )
𝑅
𝟐𝟎𝟎𝒌
=
=
𝑉𝑖𝑛 (𝑗𝜔 )
𝑗𝜔𝐿 + 𝑅 𝟐𝟎𝟎 𝒌 + 𝒋𝝎𝟎. 𝟓
(5-b)
𝑉𝑜𝑢𝑡 (𝑗𝜔 )
1
=
𝑉𝑖𝑛 (𝑗𝜔 )
1 + 𝑗𝜔 (2.5 × 10−6)
Magnitude:
|
𝑉𝑜𝑢𝑡 (𝑗𝜔 )
1
|=
𝑉𝑖𝑛 (𝑗𝜔 )
√1 + 𝜔 2 (6.25 × 10−12 )
Phase:
∠
𝑉𝑜𝑢𝑡 (𝑗𝜔 )
= − tan−1(2.5 × 10−6 𝜔 )
𝑉𝑖𝑛 (𝑗𝜔 )