This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Synthesis of R-C Network by Cauer Method”.

1. Consider the impedance functionZ(s)=( s^{2}+6s+8)/( s^{2}+3s). Find the value of R_{1} after performing the first Cauer form.

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: To find the first Cauer form, we take the continued fraction expansion by the divide, invert, divide procedure.

On performing this we get the first quotient is 1Ω.

So, R

_{1}= 1Ω.

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

a) s + 8

b) 2s + 8

c) 3s + 8

d) 4s + 8

View Answer

Explanation: The continued fraction expansion is done by the divide, invert, divide procedure. So the first reminder obtained is 3s + 8 .

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

a) 4

b) 3

c) 6

d) 9

View Answer

Explanation: On performing the continued fraction expansion we get the third quotient as 9.

So the value of R

_{2}is 9Ω.

R

_{2}= 9Ω.

4. The value of C_{1} in question 1 is?

a) 1/4

b) 1/3

c) 1/2

d) 1

View Answer

Explanation: The second quotient of the continued fraction expansion is s/3.

So the value of C

_{1}is 1/3 F.

C

_{1}= 1/3 F.

5. The value of C_{2} in question 1 is?

a) 1/6

b) 1/12

c) 1/24

d) 1/48

View Answer

Explanation: We obtain the fourth quotient on performing continued fraction expansion as s/24.

So the value of C

_{2}is 1/24 F.

C

_{2}= 1/24 F.

6. Consider the impedance function Z(s)=( s^{2}+6s+8)/( s^{2}+3s). Find the value of C_{1} after performing the second Cauer form.

a) 1/2

b) 3/8

c) 1/4

d) 1/8

View Answer

Explanation: The second Cauer network can be obtained by arranging the numerator and denominator polynomials of Z(s) in ascending powers of s. After performing the continued fraction expansion, we get

C

_{1}= 3/8 F.

7. Find the first reminder obtained by taking the continued fraction expansion in question 6.

a) 10s/3+s^{2}

b) s/3+s^{2}

c) 10s/3+3s^{2}

d) s/3+3s^{2}

View Answer

Explanation: On performing the continued fraction expansion after arranging the numerator and denominator polynomials of Z(s) in ascending powers of s, the first reminder is 10s/3+s

^{2}.

8. The value of R_{1} in question 6 is?

a) 9/10

b) 10/9

c) 8/9

d) 9/8

View Answer

Explanation: The second quotient on performing continued fraction expansion is 9/10. This is the value of 1/R

_{1}. So the value of R

_{1}is 10/9Ω.

R

_{1}= 10/9Ω.

9. The value of C_{2} in question 6 is?

a) 3

b) 3/10

c) 3/100

d) 3/1000

View Answer

Explanation: On performing continued fraction expansion, the third quotient is 100/3s. So the value of C

_{2}is 3/100 F.

C

_{2}= 3/100 F.

10. The value of R_{1} in question 6 is?

a) 10

b) 1

c) 100

d) 1000

View Answer

Explanation: The final quotient is 1/10. So the value of R

_{1}is 1/1/10.So the value of R

_{1}is 10Ω.

R

_{1}= 10Ω.

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