This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Synthesis of Reactive One-Ports by Foster’s Method”.

1. The driving point impedance of a one-port reactive network is given by Z(s)=5(s^{2}+4)(s^{2}+25)/s(s^{2}+16) . After taking the partial fractions, find the coefficient of 1/s.

a) 25/4

b) 50/4

c) 100/4

d) 125/4

View Answer

Explanation: Since there is an extra term in the numerator compared to the denominator and also an s term in the denominator, the two poles exists at 0 and infinity. Therefore the network consists of first element and last element.

By taking the partial fraction expansion of Z(s), we obtain A=5(s

^{2}+4)(s

^{2}+25)/((s

^{2}+16) ) |s=0

=(5×4×25)/16=125/4.

2. In question 1, find the coefficient of (s + j4).

a) 135/4

b) 145/4

c) 155/4

d) 165/4

View Answer

Explanation: On taking the partial fraction expansion,

B=5 (s

^{2}+4)(s

^{2}+25)/s(s-j4) |s=-j4

= 135/8.

3. The value of H from Z (s) in question 1 is?

a) 3

b) 4

c) 5

d) 6

View Answer

Explanation: By inspection, the value of H is 5.

So H = 5.

4. The value of C_{0} from the information provided in question 1 is?

a) 1/125

b) 4/125

c) 2/125

d) 3/125

View Answer

Explanation: The coefficient of 1/s is 125/4.

And C

_{0}=1/P

_{0}

= 1/(125/4)=4/125 Farad.

5. The value of L_{∞} in question 1 is?

a) 2

b) 3

c) 4

d) 5

View Answer

Explanation: We know L

_{∞}= H

= 5 H.

6. The value of C_{2} from the information provided in question 1 is?

a) 4/270

b) 8/270

c) 12/270

d) 16/270

View Answer

Explanation: We know C

_{2}= 1/2P

_{2}

= 8/(2×135)=8/270 F.

7. The value of L_{2} from the information provided in question 1 is?

a) 135/60

b) 135/62

c) 135/64

d) 135/66

View Answer

Explanation: We know L

_{2}= 2P

_{2}/ω

_{n}

^{2}

= (2×135)/(16×8)=135/64 H.

8. For performing second Foster form, after splitting the Z (S) given in question 1 into partial fractions, the coefficient of s/((s^{2}+4)) is?

a) 1/35

b) 2/35

c) 3/35

d) 4/35

View Answer

Explanation: The value of A is (1/5)(s(s

^{2}+16)))/(s-j2)(s

^{2}+25) at s=-j2

On solving we get the value of A as 2/35.

So the coefficient of s/((s

^{2}+4)) is 2/35.

9. In question 8, the coefficient of s/((s^{2}+4) ) is?

a) 4/35

b) 3/35

c) 2/35

d) 1/35

View Answer

Explanation: The coefficient of s/((s

^{2}+4) ) is B=(1/5)((s(s

^{2}+16) ))/(s-j5)(s

^{2}+4) at s=-j5. On solving we get B = 2/35.

10. Determine the value of L_{1} by performing second foster form for question 1.

a) 35/4

b) 35/3

c) 35/2

d) 35

View Answer

Explanation: P

_{1}= 2/35.

We know L

_{1}= 1/2P

_{1}

= 35/4 H.

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

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