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

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

1. Consider the impedance function, Z(s)=((s+4)(s+8))/((s+2)(s+6)). Find the value of R1 after converting into first Cauer form.
a) 1
b) 2
c) 3
d) 4

Explanation: To find out the first Cauer form, we have to take the continued fraction expansion of Z (s).
On solving, we get the first quotient as 1. So the value of R1 as 1Ω.

2. Consider the impedance function, Z(s)=((s+4)(s+8))/((s+2)(s+6)). Find the value of L2 after converting into first Cauer form.
a) 1
b) 1/2
c) 1/4
d) 1/8

Explanation: On taking the continued fraction expansion of Z (s), the second quotient is s/4. So the value of L2 is 1/4 H.
L2 = 1/4 H.

3. Consider the impedance function, Z(s)=((s+4)(s+8))/((s+2)(s+6)). Find the value of R2 after converting into first Cauer form.
a) 1/4
b) 2/4
c) 3/4
d) 4/4

Explanation: We get the third quotient on performing continued fraction expansion of Z (s) as 4/3 and is the value of 1/R2. So the value of R2 is 3/4Ω .
R2 = 3/4Ω .

4. Consider the impedance function, Z(s)=((s+4)(s+8))/((s+2)(s+6)). Find the value of L3 after converting into first Cauer form.
a) 4/3
b) 3/4
c) 4/5
d) 5/4

Explanation: The fourth quotient obtained is 3s/4. And this is the value of sL3. So the value of L3 is 3/4 H.
L3 = 3/4 H.

5. Consider the impedance function, Z(s)=((s+4)(s+8))/((s+2)(s+6)). Find the value of R3 after converting into first Cauer form.
a) 4
b) 3
c) 2
d) 1

Explanation: The value of 1/R3 (fourth quotient) obtained by continued fraction expansion 1/3. So the value of R3 is 3Ω.
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6. Consider the impedance function, Z(s)=(2s2+8s+6)/(s2+8s+12). Find the value of R1 after converting into second Cauer form.
a) 1
b) 3/4
c) 1/2
d) 1/4

Explanation: To find out the second Cauer form, we have to write the impedance function in ascending powers and by taking the continued fraction expansion of Z (s).
On solving, the first quotient obtained is 1/2. So the value of R1 as 1/2 Ω.

7. Consider the impedance function, Z(s)=(2s2+8s+6)/(s2+8s+12). Find the value of L1 after converting into second Cauer form.
a) 1/3
b) 2/3
c) 3/3
d) 4/3

Explanation: The second quotient obtained is 3/s and this is the value of 1/sL1. So the value of L1 is 1/3 H.
L1 = 1/3 H.

8. Consider the impedance function, Z(s)=(2s2+8s+6)/(s2+8s+12). Find the value of R2 after converting into second Cauer form.
a) 6/7
b) 7/6
c) 7/8
d) 8/7

Explanation: On taking the continued fraction expansion, we get third quotient as 8/7. So the value of R2 is 8/7Ω.
R2 = 8/7Ω.

9. Consider the impedance function, Z(s)=(2s2+8s+6)/(s2+8s+12). Find the value of L2 after converting into second Cauer form.
a) 5/50
b) 10
c) 5/49
d) 49/5

Explanation: We obtain the fourth quotient i.e., 1/sL2 as 49/5s. So the value of L2 is 5/49 H.
L2 = 5/49H.

10. Consider the impedance function, Z(s)=(2s2+8s+6)/(s2+8s+12). Find the value of R3 after converting into second Cauer form.
a) 1/5
b) 14/5
c) 5/14
d) 5

Explanation: The value of R3 is 14/5Ω as the fifth quotient obtained is 5/14.
R3 = 5/14Ω.

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