Network theory miscellaneous Difficult Questions and Answers | Page - 5

Network theory miscellaneous

For the circuit shown in the figure, the Thevenin voltage and resistance looking into X–Y are—

1. 4/3V, 2Ω
1. 4V, 3/2Ω
1. 4/3V, 2/3Ω
1. 4V, 2Ω

View Hint View Answer Discuss in Forum

The given circuit:

V_th Calculation:

From above figure: V_A = V_th
KCL at node A
V_A + V_A – 2i + V_A = 2
1 1 2

Also,
i = V_A = V_A
1

Now,
V_A + V_A – 2V_A + V_A = 2
1 2

or
V_A = V_th = 4V
ISC Calculation:

From above figure,
I_SC = 2A
Now,
R_th = V_th = V_OC = 4V = 2Ω
I_SC I_SC 2A

Hence alternative (D) is the correct choice.

Correct Option: D

The given circuit:

V_th Calculation:

From above figure: V_A = V_th
KCL at node A
V_A + V_A – 2i + V_A = 2
1 1 2

Also,
i = V_A = V_A
1

Now,
V_A + V_A – 2V_A + V_A = 2
1 2

or
V_A = V_th = 4V
ISC Calculation:

From above figure,
I_SC = 2A
Now,
R_th = V_th = V_OC = 4V = 2Ω
I_SC I_SC 2A

Hence alternative (D) is the correct choice.

In a two element series network, the voltage and current respectively given as,
v (t) = 50 sin (314t) + 50 sin (942t) V
i(t) = 10 sin (314t + 60°) + 8 sin (942t + 45°)
A, then the power factor of the network is approximately—

1. 0·9
1. 0·6
1. 0·3
1. 0·1

View Hint View Answer Discuss in Forum

Given,
V_(t) = 50 sin (314t) + 50 sin (942t)V
i_(t) = 10 sin (314t + 60°) + 8 sin (942t + 45°)A
Average or Real power or True power = Power of fundamental + Power of harmonics
or
P_av = 50 × 10 cos 60° + 50 × 8 cos 45°
2 2

= 125 + 100   2
Reactive Power = 50 × 10 cos 60° + 50 × 8 cos 45°
2 2

= 125   3 + 100   2
Now, Power factor = Average Power
Apparent Power

or
Power factor = 125 + 100    2
(125 + 100    2)² + (125 3 + 100    2)²

or
Power factor ≈ 0·6.

Correct Option: B

Given,
V_(t) = 50 sin (314t) + 50 sin (942t)V
i_(t) = 10 sin (314t + 60°) + 8 sin (942t + 45°)A
Average or Real power or True power = Power of fundamental + Power of harmonics
or
P_av = 50 × 10 cos 60° + 50 × 8 cos 45°
2 2

= 125 + 100   2
Reactive Power = 50 × 10 cos 60° + 50 × 8 cos 45°
2 2

= 125   3 + 100   2
Now, Power factor = Average Power
Apparent Power

or
Power factor = 125 + 100    2
(125 + 100    2)² + (125 3 + 100    2)²

or
Power factor ≈ 0·6.

For a parallel RLC resonant circuit, the damped frequency is √8 r/s and bandwidth is 2 r/s. What is its resonant frequency?

1. 2
1. √7
1. √10
1. 3

View Hint View Answer Discuss in Forum

Given,
_d = 8 r/s and B.W. = 2 r/s
From relation
_d = 0² – α²
where α = B.W.
2

or
_d² = 0² – α²
or
0² = d² + α2
or
0² = (8)² + 2/2 ²
or
0² = 8 + 1 = 9
or
0 = 3 r/s

Correct Option: D

Given,
_d = 8 r/s and B.W. = 2 r/s
From relation
_d = 0² – α²
where α = B.W.
2

or
_d² = 0² – α²
or
0² = d² + α2
or
0² = (8)² + 2/2 ²
or
0² = 8 + 1 = 9
or
0 = 3 r/s

The value of Z in figure which is most appropriate to cause parallel resonance at 500 Hz is—

1. 125·00 mH
1. 304·20 µF
1. 2·0 µF
1. 0·05 µF

View Hint View Answer Discuss in Forum

The given circuit:

f_r = 1 = 1 = 500
2π LC 2π 2 × C

or
or 1 = 25 × 10⁴
4π² 2C

or
C = 1 = 100 × 10^–6
8π² × 25 × 10⁴ 1971·92

or
C = 0·0507 µF
or
C ≈ 0·05 µF
Hence alternative (D) is the correct choice.

Correct Option: D

The given circuit:

f_r = 1 = 1 = 500
2π LC 2π 2 × C

or
or 1 = 25 × 10⁴
4π² 2C

or
C = 1 = 100 × 10^–6
8π² × 25 × 10⁴ 1971·92

or
C = 0·0507 µF
or
C ≈ 0·05 µF
Hence alternative (D) is the correct choice.

In the AC network shown in the figure, the phasor voltage V_AB (in Volts) is—

1. 0
1. 5 ∠ 30°
1. 12·5 ∠ 30°
1. 17 ∠ 30°

View Hint View Answer Discuss in Forum

The given network:
img src="http://images.interviewmania.com/wp-content/uploads/2019/05/Ans120.png">
Applying KCL at node A:
V_A + V_A = 5   30°
5 – j3 5 + j3

or
5 + j3 + 5 – j3 = 5   30°
(5 + j3) (5 – j3)

or
V_A 10 = 5   30°
25 + 9

or
V_A = 17    30°
Hence alternative (D) is the correct choice.

Correct Option: D

The given network:
img src="http://images.interviewmania.com/wp-content/uploads/2019/05/Ans120.png">
Applying KCL at node A:
V_A + V_A = 5   30°
5 – j3 5 + j3

or
5 + j3 + 5 – j3 = 5   30°
(5 + j3) (5 – j3)

or
V_A 10 = 5   30°
25 + 9

or
V_A = 17    30°
Hence alternative (D) is the correct choice.