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

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

1. Consider a function Z(s)=5(s+1)(s+4)/(s+3)(s+5). Find the value of R1 after performing the first form of Foster method.
a) 1/3
b) 2/3
c) 3/3
d) 4/3

Explanation: After splitting the given function into partial according to the properties of first form of Foster method, we get
Z(s)=4/3+(5/3)(s/(s+3))+2s/(s+5).
So, R1 = 4/3Ω.

2. Consider a function Z(s)=5(s+1)(s+4)/(s+3)(s+5). Find the value of R1.
a) 4/3
b) 5/3
c) 3/5
d) 3/4

Explanation: On taking the partial fractions, we get P1 as 5/3 and we know R1=P1. So the value of R1 is 5/3Ω.
R1 = 5/3Ω.

3. Consider a function Z(s)=5(s+1)(s+4)/(s+3)(s+5). Find the value of L1 after performing the first form of Foster method.
a) 5/9
b) 9/5
c) 4/9
d) 9/4

Explanation: We know R1=(3)(L1) and as R1 is 5/3Ω. So the value of L1 is 5/9 H.
L1 = 5/9 H.

4. Consider a function Z(s)=5(s+1)(s+4)/(s+3)(s+5). Find the value of R2 after performing the first form of Foster method.
a) 1
b) 2
c) 3
d) 4

Explanation: We obtain P2 as 2.
R2=P2.
So the value of R2 is 2Ω.
R2 = 2Ω.

5. Consider a function Z(s)=5(s+1)(s+4)/(s+3)(s+5). Find the value of L2 after performing the first form of Foster method.
a) 4/5
b) 3/5
c) 2/5
d) 1/5

Explanation: As R2=(5)(L2)
So the value of L2 is 2/5 H.
L2 = 2/5 H.
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6. Consider the admittance function, Y(s)=((2s2+16s+30))/(s2+6s+8). Determine the value of L1 after performing the second form of Foster method.
a) 1/3
b) 2/3
c) 3/3
d) 4/3

Explanation: After splitting the given function into partial according to the properties of first form of Foster method, we get Y(s)=2+3/(s+2)+1/(s+4).
We know L1=1/P1 and as P1 = 3, the value of L1 is 1/3H.
L1 = 1/3H.

7. Consider the admittance function, Y(s)=((2s2+16s+30))/(s2+6s+8). Determine the value of R1 after performing the second form of Foster method.
a) 4/3
b) 3/3
c) 2/3
d) 1/3

Explanation: R1 = 2/P1 and as P1 is 3, the value of R1 is 2/3Ω.
R1 = 2/3Ω.

8. Consider the admittance function, Y(s)=((2s2+16s+30))/(s2+6s+8). Determine the value of R2 after performing the second form of Foster method.
a) 1
b) 2
c) 3
d) 4

Explanation: On taking the partial fractions we get P2 as 1. And we know R2 = 4/P2. So the value of R2 is 4Ω.
R2 = 4Ω.

9. Consider the admittance function, Y(s)=((2s2+16s+30))/(s2+6s+8). Determine the value of L2 after performing the second form of Foster method.
a) 4
b) 1
c) 2
d) 3

Explanation: We got P2 = 1
And L2=1/P2
So the value of L2 is 1H.
L2 = 1H.

10. Consider the admittance function, Y(s)=((2s2+16s+30))/(s2+6s+8). Determine the value of R after performing the second form of Foster method.
a) 3
b) 1
c) 2
d) 4

Explanation: On performing partial fractions we get the value of R is 2Ω.
R = 2Ω.

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