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 R_{1} after converting into first Cauer form.

a) 1

b) 2

c) 3

d) 4

View Answer

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 R

_{1}as 1Ω.

2. Find the value of L_{2} in question 1.

a) 1

b) 1/2

c) 1/4

d) 1/8

View Answer

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

_{2}is ¼ H.

L

_{2}= ¼ H.

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

a) 1/4

b) 2/4

c) 3/4

d) 4/4

View Answer

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

_{2}. So the value of R

_{2}is ¾Ω .

R

_{2}= ¾Ω .

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

a) 4/3

b) 3/4

c) 4/5

d) 5/4

View Answer

Explanation: The fourth quotient obtained is 3s/4. And this is the value of sL

_{3}. So the value of L

_{3}is ¾ H.

L

_{3}= ¾ H.

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

a) 4

b) 3

c) 2

d) 1

View Answer

Explanation: The value of 1/R

_{3}(fourth quotient) obtained by continued fraction expansion 1/3. So the value of R

_{3}is 3Ω.

6. Consider the impedance function; Z(s)=(2s^{2}+8s+6)/( s^{2}+8s+12). Find the value of R_{1} after converting into second Cauer form.

a) 1

b) 3/4

c) 1/2

d) 1/4

View Answer

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 R

_{1}as ½ Ω.

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

a) 1/3

b) 2/3

c) 3/3

d) 4/3

View Answer

Explanation: The second quotient obtained is 3/s and this is the value of 1/sL

_{1}. So the value of L

_{1}is 1/3 H.

L

_{1}= 1/3 H.

8. Find the value of R_{2} in question 6.

a) 6/7

b) 7/6

c) 7/8

d) 8/7

View Answer

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

_{2}is 8/7Ω.

R

_{2}= 8/7Ω.

9. Find the value of L_{2} in question 6.

a) 5/50

b) 10

c) 5/49

d) 49/5

View Answer

Explanation: We obtain the fourth quotient i.e., 1/sL

_{2}as 49/5s. So the value of L

_{2}is 5/49 H.

L

_{2}= 5/49H.

10. Find the value of R_{3} in question 6.

a) 1/5

b) 14/5

c) 5/14

d) 5

View Answer

Explanation: The value of R

_{3}is 14/5Ω as the fifth quotient obtained is 5/14.

R

_{3}= 5/14Ω.

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