This set of Network Theory Questions and Answers for Aptitude test focuses on “Synthesis of Reactive One-Ports by Cauer Method”.
1. The driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form, find the value of L1.
a) s
b) 2s
c) 3s
d) 4s
View Answer
Explanation: The first Cauer form of the network is obtained by taking the continued fraction expansion of given Z(s). And we get he first quotient as 2s.
So, L1 = 2s.
2. Find the first reminder obtained by taking the continued fraction expansion in the driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form.
a) 4s3+10s
b) 12s3+10s
c) 4s3+16s
d) 12s3+16s
View Answer
Explanation: On taking the continued fraction expansion, the first reminder obtained is 4s3+10s.
3. The driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form, find the value of C2.
a) 1
b) 1/2
c) 1/3
d) 1/4
View Answer
Explanation: The second quotient obtained on taking the continued fraction expansion is s/4 and this is the value of sC2. So the value of C2 = 1/4.
4. The driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form, find the value of L3.
a) 8
b) 8/3
c) 8/5
d) 8/7
View Answer
Explanation: By taking the continued fraction expansion, the third quotient is 8s/3.
sL3 = 8s/3.
So L3 = 8/3H.
5. The driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form, find the value of C4.
a) 1/2
b) 1/4
c) 3/4
d) 1
View Answer
Explanation: We get the fourth quotient as 3s/4.
So sC4 = 3s/4.
C4 = 3/4F.
6. The driving point impedance of an LC network is given by Z(s)=(2s5+12s3+16s)/(s4+4s2+3). By taking the continued fraction expansion using first Cauer form, find the value of L5.
a) 2
b) 2/5
c) 2/7
d) 2/3
View Answer
Explanation: On taking the continued fraction expansion fifth quotient is 2s/3.
sL5 = 2s/3
So L5 = 2/3H.
7. The driving point impedance of an LC network is given by Z(s)=(s4+4s2+3)/(s3+2s). By taking the continued fraction expansion using second Cauer form, find the value of C1.
a) 2/3
b) 2/2
c) 1/2
d) 4/2
View Answer
Explanation: To obtain the second Cauer form, we have to arrange the numerator and the denominator of given Z(s) in ascending powers of s before starting the continued fraction expansion.
By taking the continued fraction expansion we get the first quotient as 3/2s.
So 1/sC1 = 3/2s
C1 = 2/3F.
8. The driving point impedance of an LC network is given by Z(s)=(s4+4s2+3)/(s3+2s). By taking the continued fraction expansion using second Cauer form, find the value of L2.
a) 1/5
b) 2/5
c) 3/5
d) 5/4
View Answer
Explanation: On taking the continued fraction expansion the second quotient is 4/5s.
1/sL2 = 4/5s
So L2 = 5/4H.
9. The driving point impedance of an LC network is given by Z(s)=(s4+4s2+3)/(s3+2s). By taking the continued fraction expansion using second Cauer form, find the value of C3.
a) 25/s
b) 2/25s
c) 25/3s
d) 25/4s
View Answer
Explanation: The third quotient is 25/2s.
1/sC3 = 25/2s.
C3 = 2/25F.
10. The driving point impedance of an LC network is given by Z(s)=(s4+4s2+3)/(s3+2s). By taking the continued fraction expansion using second Cauer form, find the value of L4.
a) 5
b) 2/5
c) 3/5
d) 4/5
View Answer
Explanation: We obtain the fourth quotient as 1/5s.
1/sL4 = 1/5s
L4 = 5H.
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