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

This set of Network Theory Assessment Questions and Answers focuses on “Synthesis of R-C Network by Foster Method”.

1. Consider the impedance function Z(s)=3(s+2)(s+4)/(s+1)(s+3). Find the value of R1 after realizing by first Foster method.
a) 9/2
b) 2/9
c) 9
d) 1/9

Explanation: The first Foster form can be realized by taking the partial fraction of Z (s).
On solving, we get
Z (s)=3+(9/2/(s+1))+(3/2/(s+3)).
So the value of R1 is 9/2Ω.

2. Consider the impedance function Z(s)=3(s+2)(s+4)/(s+1)(s+3). Find the value of C1 after realizing by first Foster method.
a) 1/9
b) 9
c) 2/9
d) 9/2

Explanation: After taking the partial fractions, as P1 = 1/C1, we get the 1/C1 value as 9/2. So the value of C1 is 2/9 F.
C1 = 2/9 F.

3. Consider the impedance function Z(s)=3(s+2)(s+4)/(s+1)(s+3). Find the value of C2 after realizing by first Foster method.
a) 1/3
b) 3
c) 3/2
d) 2/3

Explanation: We know P2 = 1/C2. The value of P2 is 3/2. So the value of C2 is 2/3 F.
C2 = 2/3 F.

4. Consider the impedance function Z(s)=3(s+2)(s+4)/(s+1)(s+3). Find the value of R2 after realizing by first Foster method.
a) 1
b) 1/2
c) 1/4
d) 1/8

Explanation: We got 1/R2C2 = 3. And the value of C2 is 2/3 F. So the value of R2 is 1/2 Ω.
R2 = 1/2 Ω.

5. Consider the impedance function Z(s)=3(s+2)(s+4)/(s+1)(s+3). Find the value of R after realizing by first Foster method.
a) 1
b) 2
c) 3
d) 4

Explanation: On taking partial fraction of Z(s), we get the value of R is 3Ω.
R = 3Ω.
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6. Consider the impedance function Y(s)=(s2+4s+3)/(3s2+18s+24). Find the value of R0 after realizing by second Foster method.
a) 4
b) 8
c) 12
d) 16

Explanation: The second Foster Form can be realized by taking the reciprocal of the impedance function and by taking partial fractions. So we get 1/R0 as 1/8. So the value of R0 is 8Ω.
R0 = 8Ω.

7. Consider the impedance function Y(s)=(s2+4s+3)/(3s2+18s+24). Find the value of R1 after realizing by second Foster method.
a) 16
b) 12
c) 8
d) 4

Explanation: On taking the partial fractions we get P1 as 1/12. And we know that R1=1/P1. So the value of R1 is 12Ω.
R1 = 12Ω.

8. Consider the impedance function Y(s)=(s2+4s+3)/(3s2+18s+24). Find the value of C1 after realizing by second Foster method.
a) 1/24
b) 1/12
c) 1/6
d) 1/3

Explanation: The value of C1 is 1/((2)(R1)). As R1 is 12Ω, the value of C1 is 1/24 F.
C1 = 1/24 F.

9. Consider the impedance function Y(s)=(s2+4s+3)/(3s2+18s+24). Find the value of R2 after realizing by second Foster method.
a) 5
b) 6
c) 7
d) 8

Explanation: We get the value of P2 on taking the partial fractions as 1/8. And we know R2 = 1/P2 So the value of R2 is 8Ω.
So, R2 = 8Ω.

10. Consider the impedance function Y(s)=(s2+4s+3)/(3s2+18s+24). Find the value of C2 after realizing by second Foster method.
a) 1/16
b) 1/8
c) 1/32
d) 1/64

Explanation: We obtained R2 as 8Ω and we know C2 = 1/((4)(R2)). So the value of C2 is 1/32 F.
C2 = 1/32 F.

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