Network theory miscellaneous Moderate Questions and Answers | Page - 12

Network theory miscellaneous

Which of the following are the conditions for a two port passive network to be a reciprocal one?
1. Z₁₂ = z₂₁
2. Y₁₂ = y₂₁
3. h₁₂ = – h₂₁
Select the correct condition from the code given below—

1. Only 1 and 2
1. Only 2 and 3
1. Only 1 and 3
1. 1, 2 and 3

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For the two port passive network to be reciprocal
1. Z₁₂ = Z₂₁ → correct
2. Y₁₂ = Y₂₁ → correct
3. h₁₂ = h_-21 → correct

(D) is the correct choice.

Correct Option: D

For the two port passive network to be reciprocal
1. Z₁₂ = Z₂₁ → correct
2. Y₁₂ = Y₂₁ → correct
3. h₁₂ = h_-21 → correct

(D) is the correct choice.

What is the open circuit impedance Z₁₁(s) of the network shown in the figure given above?

1. 10 + 2s
1. 10 - 4
  s
1. 10 + 4
  s
1. 10 – 2s

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The given network:

Applying KVL in the input side
V₁ = l₁ × 10 + l₁ = 1 + l₂ 1
1 s 1 s
4 4

or
V₁ = 10l₂ + 4 l₁ + l₂ 4
s s

or
V₁ = I₁ 10 + 4 + 4 l²........(i)
s s

On comparing equation (i) with standard equation of Z-parameters, we get
Z₁₁ = 10 + 4 l². . . . .. . . . (ii)
s

Hence alternative (C) is the correct choice.

Correct Option: A

The given network:

Applying KVL in the input side
V₁ = l₁ × 10 + l₁ = 1 + l₂ 1
1 s 1 s
4 4

or
V₁ = 10l₂ + 4 l₁ + l₂ 4
s s

or
V₁ = I₁ 10 + 4 + 4 l²........(i)
s s

On comparing equation (i) with standard equation of Z-parameters, we get
Z₁₁ = 10 + 4 l². . . . .. . . . (ii)
s

Hence alternative (C) is the correct choice.

What is the value of Z₂₁ for the network shown above?

1. – 2Ω
1. – 1/2Ω
1. 1Ω
1. 2Ω

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The given network

Since the given network is symmetric lattice network,
therefore
Z₁₁ = Z₂₂ = R₁ + R₂ = 2 + 1 = 3 Ω
2 2 2

and
Z₁₁ = Z₂₁ = R₂ - R₁ = 1 - 2 = -1 Ω
2 2 2

Hence alternative (B) is the correct choice.

Correct Option: B

The given network

Since the given network is symmetric lattice network,
therefore
Z₁₁ = Z₂₂ = R₁ + R₂ = 2 + 1 = 3 Ω
2 2 2

and
Z₁₁ = Z₂₁ = R₂ - R₁ = 1 - 2 = -1 Ω
2 2 2

Hence alternative (B) is the correct choice.

Equivalent π network The currents I₁ and I₂ at the output of 2-port network can be written as
I₁ = 5V₁ – V₂
I₂ = – V₁ + V₂
Which one of the following gives the parameters of an equivalent π network shown above?

1. y₁ = 4Ω, y₂ = 0, y₃ = 1Ω
1. y₁ = 4Ω, y₂ = 4, y₃ = 1Ω
1. y₁ = 1Ω, y₂ = 1Ω, y₃ = 1Ω
1. y₁ = 4Ω, y₂ = 0, y₃ = 2Ω

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The Y-parameter are represented by expressions:
I₁ = Y₁₁V₁ + Y₁₂V₂ . . . …(i)
I₂ = Y₂₁V₁ + Y₂₂V₂ . . . …(ii)
The given network:

The given equation
I₁ = 5V₁ – V₂ . . . …(iii)
I₂ = – V₁ + V₂ . . . …(iv)
On comparing equation (i) and (ii) with (iii) and (iv), we get:
y₁₁ = 5, y₁₂ = – 1
y₂₁ = – 1, y₂₂ = 1
For a π-network
y₁₁ = y₁ + y₃ = 5
y₂₂ = y₂ + y₃ = 1
y₁₂ = y₂₁ = – y₃ = – 1, i.e., y₃ = 1Ω
So,
y₁ = 5 – y₃ = 5 – 1 = 4Ω
and
y₂ = 1 – y₃ = 1 – 1 = 0Ω
Hence alternative (A) is the correct choice.

Correct Option: A

The Y-parameter are represented by expressions:
I₁ = Y₁₁V₁ + Y₁₂V₂ . . . …(i)
I₂ = Y₂₁V₁ + Y₂₂V₂ . . . …(ii)
The given network:

The given equation
I₁ = 5V₁ – V₂ . . . …(iii)
I₂ = – V₁ + V₂ . . . …(iv)
On comparing equation (i) and (ii) with (iii) and (iv), we get:
y₁₁ = 5, y₁₂ = – 1
y₂₁ = – 1, y₂₂ = 1
For a π-network
y₁₁ = y₁ + y₃ = 5
y₂₂ = y₂ + y₃ = 1
y₁₂ = y₂₁ = – y₃ = – 1, i.e., y₃ = 1Ω
So,
y₁ = 5 – y₃ = 5 – 1 = 4Ω
and
y₂ = 1 – y₃ = 1 – 1 = 0Ω
Hence alternative (A) is the correct choice.

In the circuit shown below, RL will absorb maximum power when its value is—

1. 2·75Ω
1. 7·5Ω
1. 25Ω
1. 27Ω

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The given circuit

R_L will absorb maximum power when its value is equivalent to R_th i.e., R_L = R_th
The R_th can be calculated by the equivalent circuit shown below

Correct Option: C

The given circuit

R_L will absorb maximum power when its value is equivalent to R_th i.e., R_L = R_th
The R_th can be calculated by the equivalent circuit shown below