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)=(2s^{5}+12s^{3}+16s)/( s^{4}+4s^{2}+3). By taking the continued fraction expansion using first Cauer form, find the value of L_{1}.

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, L

_{1}= 2s.

2. Find the first reminder obtained by taking the continued fraction expansion in question 1.

a) 4s^{3}+10s

b) 12s^{3}+10s

c) 4s^{3}+16s

d) 12s^{3}+16s

View Answer

Explanation: On taking the continued fraction expansion, the first reminder obtained is 4s

^{3}+10s.

3. Find the value of C_{2} in question 1.

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 sC

_{2}. So the value of C

_{2}= 1/4.

4. Find the value of L_{3} in question 1.

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.

sL

_{3}= 8s/3.

So L

_{3}= 8/3H.

5. Find the value of C_{4} in question 1.

a) 1/2

b) 1/4

c) 3/4

d) 1

View Answer

Explanation: We get the fourth quotient as 3s/4.

So sC

_{4}= 3s/4.

C

_{4}= 3/4F.

6. Find the value of L_{5} in question 1.

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.

sL

_{5}= 2s/3

So L

_{5}= 2/3H.

7. The driving point impedance of an LC network is given by Z(s)=(s^{4}+4s^{2}+3)/(s^{3}+2s) . By taking the continued fraction expansion using second Cauer form, find the value of C_{1}.

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/sC

_{1}= 3/2s

C

_{1}= 2/3F..

8. Find the value of L_{2} in question 7.

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/sL

_{2}= 4/5s

So L

_{2}= 5/4H.

9. Find the value of C_{3} in question 7.

a) 25/s

b) 2/25s

c) 25/3s

d) 25/4s

View Answer

Explanation: The third quotient is 25/2s.

1/sC

_{3}= 25/2s.

C

_{3}= 2/25F.

10. Find the value of L_{4} in question 7.

a) 5

b) 2/5

c) 3/5

d) 4/5

View Answer

Explanation: We obtain the fourth quotient as 1/5s.

1/sL

_{4}= 1/5s

L

_{4}= 5H.

**Sanfoundry Global Education & Learning Series – Network Theory.**

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