# Network Theory Questions and Answers – Synthesis of Reactive One-Ports by Foster’s Method

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(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, find the coefficient of 1/s.
a) 25/4
b) 50/4
c) 100/4
d) 125/4

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(s2+4)(s2+25)/((s2+16))|s=0
=(5×4×25)/16=125/4.

2. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, find the coefficient of (s + j4).
a) 135/4
b) 145/4
c) 155/4
d) 165/4

Explanation: On taking the partial fraction expansion,
B=5 (s2+4)(s2+25)/s(s-j4)|s=-j4
= 135/8.

3. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, what is the value of H from Z (s)?
a) 3
b) 4
c) 5
d) 6

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

4. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, what is the value of C0?
a) 1/125
b) 4/125
c) 2/125
d) 3/125

Explanation: The coefficient of 1/s is 125/4.
And C0=1/P0

5. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, what is the value of L?
a) 2
b) 3
c) 4
d) 5

Explanation: We know L = H
= 5 H.
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6. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, what is the value of C2?
a) 4/270
b) 8/270
c) 12/270
d) 16/270

Explanation: We know C2 = 1/2P2
= 8/(2×135)=8/270 F.

7. The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16). After taking the partial fractions, what is the value of L2?
a) 135/60
b) 135/62
c) 135/64
d) 135/66

Explanation: We know L2 = 2P2n2
= (2×135)/(16×8)=135/64 H.

8. For performing second Foster form, after splitting the Z (S) in The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16), what is the coefficient of s/((s2+4)) is?
a) 1/35
b) 2/35
c) 3/35
d) 4/35

Explanation: The value of A is (1/5)(s(s2+16)))/(s-j2)(s2+25) at s=-j2
On solving we get the value of A as 2/35.
So the coefficient of s/((s2+4)) is 2/35.

9. For performing second Foster form, after splitting the Z (S) in The driving point impedance of a one-port reactive network is given by Z(s)=5(s2+4)(s2+25)/s(s2+16), what is the coefficient of s/((s2+4)) is?
a) 4/35
b) 3/35
c) 2/35
d) 1/35

Explanation: The coefficient of s/((s2+4)) is B=(1/5)((s(s2+16)))/(s-j5)(s2+4) at s=-j5. On solving we get B = 2/35.

10. Determine the value of L1 by performing second foster form for Z(s)=5(s2+4)(s2+25)/s(s2+16).
a) 35/4
b) 35/3
c) 35/2
d) 35

Explanation: P1 = 2/35.
We know L1 = 1/2P1
= 35/4 H.

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