# Network Theory Questions and Answers – Synthesis of R-C Network by Cauer Method

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)=(s2+6s+8)/(s2+3s). Find the value of R1 after performing the first Cauer form.
a) 1
b) 2
c) 3
d) 4

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, R1 = 1Ω.

2. Consider the impedance functionZ(s)=(s2+6s+8)/(s2+3s). Find the first reminder obtained by taking the continued fraction expansion after performing the first Cauer form.
a) s + 8
b) 2s + 8
c) 3s + 8
d) 4s + 8

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

3. Consider the impedance functionZ(s)=(s2+6s+8)/(s2+3s). Find the value of R2 after performing the first Cauer form.
a) 4
b) 3
c) 6
d) 9

Explanation: On performing the continued fraction expansion we get the third quotient as 9.
So the value of R2 is 9Ω.
R2 = 9Ω.

4. Consider the impedance functionZ(s)=(s2+6s+8)/(s2+3s). Find the value of C1 after performing the first Cauer form.
a) 1/4
b) 1/3
c) 1/2
d) 1

Explanation: The second quotient of the continued fraction expansion is s/3.
So the value of C1 is 1/3 F.
C1 = 1/3 F.

5. Consider the impedance functionZ(s)=(s2+6s+8)/(s2+3s). Find the value of C2 after performing the first Cauer form.
a) 1/6
b) 1/12
c) 1/24
d) 1/48

Explanation: We obtain the fourth quotient on performing continued fraction expansion as s/24.
So the value of C2 is 1/24 F.
C2 = 1/24 F.

6. Consider the impedance function Z(s)=(s2+6s+8)/(s2+3s). Find the value of C1 after performing the second Cauer form.
a) 1/2
b) 3/8
c) 1/4
d) 1/8

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
C1 = 3/8 F.

7. Consider the impedance function Z(s)=(s2+6s+8)/(s2+3s). Find the first reminder obtained by taking the continued fraction expansion after performing the second Cauer form.
a) 10s/3+s2
b) s/3+s2
c) 10s/3+3s2
d) s/3+3s2

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+s2.

8. Consider the impedance function Z(s)=(s2+6s+8)/(s2+3s). Find the value of R1 after performing the second Cauer form.
a) 9/10
b) 10/9
c) 8/9
d) 9/8

Explanation: The second quotient on performing continued fraction expansion is 9/10. This is the value of 1/R1. So the value of R1 is 10/9Ω.
R1 = 10/9Ω.

9. Consider the impedance function Z(s)=(s2+6s+8)/(s2+3s). Find the value of C2 after performing the second Cauer form.
a) 3
b) 3/10
c) 3/100
d) 3/1000

Explanation: On performing continued fraction expansion, the third quotient is 100/3s. So the value of C2 is 3/100 F.
C2 = 3/100 F.

10. Consider the impedance function Z(s)=(s2+6s+8)/(s2+3s). Find the value of R1 after performing the second Cauer form.
a) 10
b) 1
c) 100
d) 1000

Explanation: The final quotient is 1/10. So the value of R1 is 1/1/10.So the value of R1 is 10Ω.
R1 = 10Ω.

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