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## Network Theory MCQ Set 1

1. Superposition theorem states that the response in any element is the ____________ of the responses that can be expected to flow if each source acts independently of other sources.
a) algebraic sum
b) vector sum
c) multiplication
d) subtraction

Answer: b [Reason:] The superposition theorem is used to analyse ac circuits containing more than one source. Superposition theorem states that the response in any element is the vector sum of the responses that can be expected to flow if each source acts independently of other sources.

2. Superposition theorem is valid for only linear systems.
a) true
b) false

Answer: a [Reason:] Superposition theorem is valid for only linear systems. Superposition theorem is not valid for non-linear systems. In a network containing complex impedance, all quantities must be treated as complex numbers.

3. Determine the current through (2+j5) Ω impedance considering 50∠0⁰ voltage source.

a) 6.42∠77.47⁰
b) 6.42∠-77.47⁰
c) 5.42∠77.47⁰
d) 5.42∠-77.47⁰

Answer: d [Reason:] According to the superposition theorem the current due to the 50∠0o source is I1 with the current source 20∠30⁰ A short-circuited. I1 = (50∠0o)/(2+j4+j5) = 5.42∠-77.47o A.

4. Find the voltage across (2+j5) Ω impedance considering 50∠0⁰ voltage source.
a) 30.16∠-9.28⁰
b) 30.16∠9.28⁰
c) 29.16∠-9.28⁰
d) 29.16∠9.28⁰

Answer: c [Reason:] Voltage across (2+j5) Ω impedance considering 50∠0⁰ voltage source is V1 = 5.42∠-77.47o (2+j5) = 29.16∠-9.28o V.

5. Find the current through (2+j5) Ω impedance considering 20∠30⁰ voltage source.
a) 8.68∠-42.53⁰
b) 8.68∠42.53⁰
c) 7.68∠42.53⁰
d) 7.68∠-42.53⁰

Answer: b [Reason:] The current through (2+j5) Ω impedance considering 20∠30⁰ voltage source is I2 = 20∠30o×j4/(2+j9) = 8.68∠42.53o A.

6. Determine the voltage across (2+j5) Ω impedance considering 20∠30⁰ voltage source.
a) 45.69∠-110.72⁰
b) 45.69∠110.72⁰
c) 46.69∠-110.72⁰
d) 46.69∠110.72⁰

Answer: d [Reason:] The voltage across (2+j5) Ω impedance considering 20∠30⁰ voltage source is V2 = 8.68∠42.53o (2+j5) = 46.69∠110.72⁰V.

7. Find the voltage across (2+j5) Ω impedance using Superposition theorem.
a) 40.85∠72.53⁰
b) 40.85∠-72.53⁰
c) 41.85∠72.53⁰
d) 41.85∠-72.53⁰

Answer: a [Reason:] The voltage across (2+j5) Ω impedance using Superposition theorem is the sum of the voltages V1 and V2. => V = V1+V2 = 29.16∠-9.28o+46.69∠110.72o=40.85∠72.53o V.

8. Determine the voltage Vab considering the source 50∠0⁰V.

a) 50∠0⁰
b) 4∠0⁰
c) 54∠0⁰
d) 46∠0⁰

Answer: a [Reason:] Let source 50∠0⁰ act on the circuit and set the source 4∠0⁰A equal to zero. If the current source is zero, it becomes open-circuited. Then the voltage across ‘ab’ is 50∠0⁰.

9. Determine the voltage Vab considering the source 4∠0⁰A in the circuit shown above.
a) 46∠0⁰
b) 4∠0⁰
c) 54∠0⁰
d) 50∠0⁰

Answer: b [Reason:] Set the voltage source 50∠0⁰V to zero, and is short-circuited. So, the voltage drop across ‘ab’ is zero.

10. Find the voltage Vab in the circuit shown above using Superposition theorem.
a) 4∠0⁰
b) 50∠0⁰
c) 54∠0⁰
d) 46∠0⁰

Answer: b [Reason:] The total voltage is the sum of the two voltages V1 and V2 => Vab = V1+V2 = 50∠0⁰V.

## Network Theory MCQ Set 2

1. For the tank circuit shown below, find the resonant frequency.

a) 157.35
b) 158.35
c) 159.35
d) 160.35

Answer: b [Reason:] The parallel resonant circuit is generally called a tank circuit because of the fact that the circuit stores energy in the magnetic field of the coil and in the electric field of the capacitor. The resonant frequency fr = (1/2π) √((1/LC)-(R2/L2 ) ).

2. The expression of ωr in parallel resonant circuit is?
a) 1/(2√LC)
b) 1/√LC
c) 1/(π√LC)
d) 1/(2π√LC)

Answer: b [Reason:] The stored energy is transferred back and forth between the capacitor and coil and vice-versa. The expression of ωr in parallel resonant circuit is ωr = 1/√LC.

3. The expression of bandwidth for parallel resonant circuit is?
a) 1/RC
b) RC
c) 1/R
d) 1/C

Answer: a [Reason:] The expression of bandwidth for parallel resonant circuit is BW = 1/RC. the circuit is said to be in resonant condition when the susceptance part of admittance is zero.

4. The quality factor in case of parallel resonant circuit is?
a) C
b) ωrRC
c) ωrC
d) 1/ωrRC

Answer: d [Reason:] The quality factor in case of parallel resonant circuit is Q = 1/ωrRC. The impedance of parallel resonant circuit is maximum at the resonant frequency and decreases at lower and higher frequencies.

5. The quality factor is the product of 2π and the ratio of ______ to _________
a) maximum energy stored, energy dissipated per cycle
b) energy dissipated per cycle, maximum energy stored
c) maximum energy stored per cycle, energy dissipated
d) energy dissipated, maximum energy stored per cycle

Answer: a [Reason:] At low frequencies XL is very small and XC is very large so the total impedance is essentially inductive. The quality factor is the product of 2π and the ratio of maximum energy stored to energy dissipated per cycle.

6. The maximum energy stored in a capacitor is?
a) CV2
b) CV2/2
c) CV2/4
d) CV2/8

Answer: b [Reason:] The maximum energy stored in a capacitor is CV2/2. Maximum energy = CV2/2. As frequency increases the impedance also increases and the inductive reactance dominates until the resonant frequency is reached.

7. The expression of quality factor is?
a) IL/I
b) I/IL
c) IL
d) I

Answer: a [Reason:] The expression of quality factor is IL/I. Quality factor = IL/I. At the the point XL = XC, the impedance is at its maximum.

8. The quality factor is defined as?
a) I
b) IC
c) I/IC
d) IC/I

Answer: d [Reason:] The quality factor is defined as IC/I. Quality factor = IC/I. As the frequency goes above resonance capacitive reactance dominates and impedance decreases.

9. In the circuit shown in the figure, an inductance of 0.1H having a Q of 5 is in parallel with a capacitor. Determine the value coil resistance (Ω) of at a resonant frequency of 500 rad/sec.

a) 10
b) 20
c) 30
d) 40

Answer: a [Reason:] Quality factor Q = ωrL/R. L = 0.1H, Q = 5, ωr = 500 rad/sec. On solving, R = 10Ω. While plotting the voltage and current variation with frequency, at resonant frequency, the current is maximum.

10. Find the value of capacitance (µF) in the circuit shown in the question 9.
a) 10
b) 20
c) 30
d) 40

Answer: d [Reason:] ω2r = 1/LC. L = 0.1H, ωr = 500 rad/sec. On solving, C = 40 µF. In order to tune a parallel circuit to a lower frequency the capacitance must be increased.

## Network Theory MCQ Set 3

1. The dual pair of current is?
a) voltage
b) current source
c) capacitance
d) conductance

Answer: a [Reason:] In an electrical circuit itself there are pairs of terms which can be interchanged to get new circuits. The dual pair of current is voltage. And the dual pair of voltage is current.

2. The dual pair of capacitance is?
a) capacitance
b) resistance
c) current source
d) inductance

Answer: d [Reason:] The dual pair of inductance is capacitance. And the dual pair of capacitance is inductance.In an electrical circuit itself there are pairs of terms which can be interchanged to get new circuits.

3. The dual pair of resistance is?
a) inductance
b) capacitance
c) conductance
d) current

Answer: c [Reason:] The dual pair of resistance is conductance. And the dual pair of conductance is resistance.

4. The dual pair of voltage source is?
a) voltage
b) current source
c) current
d) resistance

Answer: b [Reason:] The dual pair of voltage source is current source. And the dual pair of current source is voltage source.

5. The dual pair of KCL is?
a) KVL
b) current
c) voltage
d) current source

Answer: a [Reason:] In an electrical circuit itself there are pairs of terms which can be interchanged to get new circuits. The dual pair of KCL is KVL. And the dual pair of KVL is KCL.

6. Tellegen’s Theorem is valid for _____ network?
a) linear or non-linear
b) passive or active
c) time variant or time invariant
d) all the above

Answer: d [Reason:] Tellegen’s Theorem is valid for any lumped network. So, Tellegan’s theorem is valid for linear or non-linear networks, passive or active networks and time variant or time invariant networks.

7. For Tellegan’s Theorem to satisfy, the algebraic sum of the power delivered by the source is _____ than power absorbed by all elements.
a) greater
b) less
c) equal
d) greater than or equal

Answer: c [Reason:] For Tellegan’s Theorem to satisfy, algebraic sum of the power delivered by the source equal to power absorbed by all elements. All branch currents and voltages in that network must satisfy Kirchhoff’s laws.

8. Consider the circuit shown below. Find whether the circuit satisfies Tellegan’s theorem.

a) satisfies
b) does not satisfy
c) satisfies partially
d) satisfies only for some elements

Answer: a [Reason:] i1=i2=2A, i3=2A. V1=-2V, V2=-8V, V3=10V. Algebraic sum =

9. The circuit shown below satisfies Tellegen’s theorem.

a) True
b) False

Answer: a [Reason:] i1=i2=4A, i3=4A. V1=-20V, V2=0V, V3=20V. Algebraic sum =

10. If two networks have same graph with different type of elements between corresponding nodes, then?

Answer: a [Reason:] If two networks have same graph with different type of elements between corresponding nodes, then

## Network Theory MCQ Set 4

1. Calculate the Z –parameter Z11 in the circuit shown below.

a) 1.5
b) 2.5
c) 3.5
d) 4.5

Answer: b [Reason:] The Z –parameter Z11 is V1/I1, port 2 is open circuited. V1 = (1+1.5)I1 => V1/I1 = 2.5 and on substituting, we get Z11 = 2.5Ω.

2. Determine the Z-parameter Z12 in the circuit shown in question 1.
a) 1
b) 2
c) 3
d) 4

Answer: a [Reason:] The Z-parameter Z12 is V2/I1 |I2=0. On open circuiting port 2 we obtain the equation, V1 = (1.5) I2 => V1/I1 = 1.5. On substituting we get Z12 = 1.5Ω.

3. Determine the Z-parameter Z21 in the circuit shown in question 1.
a) 4
b) 3
c) 2
d) 1

Answer: d [Reason:] The Z-parameter Z21 is V2/I1 |I2=0. On open circuiting port 2, we get V2 = (1.5)I1 => V2/I1 = 1.5. On substituting we get Z21 = 1.5Ω.

4. Determine the Z-parameter Z22 in the circuit shown in question 1.
a) 1
b) 3
c) 2
d) 4

Answer: c [Reason:] The Z-parameter Z21 is V2/I2 |I1=0. This parameter is obtained by open circuiting port 1. So we get V2 = ((2+2)||4)I2 => V2 = 2(I2) => V2/I2 = 2. On substituting Z21 = 2Ω.

5. Find the value of V1/I1 in the circuit shown in question 1.
a) 1.25
b) 2.25
c) 3.25
d) 4.25

Answer: b [Reason:] We have the relation V1/I1=Z11– Z12Z21/(ZL+Z21) and ZL is the load impedance and is equal to 2Ω. On solving V1/I1=2.5-1/(2+2)=2.25Ω.

6. Determine the input impedance of the network shown in question 1.
a) 4.25
b) 3.25
c) 2.25
d) 1.25

Answer: b [Reason:] From the figure by inspection we can say that the source resistance is 1Ω. So Zin = (V1/I1) + Source resistance. We had V1/I1 = 2.25. On substituting Zin=1+2.25=3.25Ω.

7. Determine the value of source admittance in the circuit shown below.

a) 1
b) 2
c) 3
d) 4

Answer: a [Reason:] From the figure the value of the admittance parallel to the current source is 1 mho and this is the value of source admittance. So Ys = 1 mho.

8. Find the value of I2/V2 in the circuit shown in question 7.
a) 7/6
b) 6/7
c) 7/12
d) 12/7

Answer: c [Reason:] The relation between I2/V2 and Y-parameters is I2/V2=(5/8×1+5/8×1/2-1/16)/(1+1/2)=7/12 mho.

9. The value of the Y-parameter Y22 in the circuit shown in question 7.
a) 12/7
b) 6/7
c) 7/6
d) 7/12

Answer: d [Reason:] The relation between Y22 and I2/V2 is Y22= I2/V2. We have the relation I2/V2 = (Y22Ys+Y22Y11-Y21Y12)/(Ys+Y11). On substituting their values in the equation we get Y22 = 7/12 mho.

10. The value of the Z-parameter Z22 in the circuit shown in question 7.
a) 6/7
b) 7/12
c) 12/7
d) 7/6

Answer: c [Reason:] The Z-parameter Z22 is inverse of the Y-parameter Y22 i.e., Z22 = 1/Y22. We got Y22 = 7/12. So on substituting we get Z22 = 12/7 mho.

## Network Theory MCQ Set 5

1. The condition for maximum voltage to be transferred to the load is?
a) Source resistance greater than load resistance
b) Source resistance less than load resistance
c) Source resistance equal to load resistance
d) Source resistance greater than or equal to load resistance

Answer: b [Reason:] Our aim is to find the necessary conditions so that the power delivered by the source to the load is maximum. The condition for maximum voltage to be transferred to the load is source resistance less than load resistance.

2. The condition for maximum current to be transferred to the load is?
a) Source resistance greater than or equal to load resistance
b) Source resistance equal to load resistance
c) Source resistance less than load resistance
d) Source resistance greater than load resistance

Answer: d [Reason:] The condition for maximum current to be transferred to the load is source resistance greater than load resistance. For many applications an important consideration is the maximum power transfer to the load.

3. The condition for maximum power to be transferred to the load is?
a) Source resistance equal to load resistance
b) Source resistance greater than load resistance
c) Source resistance greater than or equal to load resistance
d) Source resistance less than load resistance

Answer: a [Reason:] The condition for maximum power to be transferred to the load is source resistance equal to load resistance. Maximum power transfer is desirable from the output amplifier to the speaker of an audio sound system.

4. In the circuit shown determine the value of load resistance when the load resistance draws maximum power?

a) 50
b) 25
c) 75
d) 100

Answer: b [Reason:] The source delivers maximum power when load resistance is equal to source resistance. So, load resistance = 25Ω.

5. Find the value of the maximum power in the circuit shown in the question 4.
a) 25
b) 50
c) 75
d) 100

Answer: a [Reason:] Current = 50/(25+25)=1A. Maximum power delivered to load = (I)2 ×RL. On substituting the values obtained and given we get maximum power in the circuit is (1)2 ×25=25W.

6. If the source ZS is complex, then the condition for the maximum power to be transferred is?
a) ZL=ZS
b) ZL=ZS*
c) ZL=-ZS
d) ZL=-ZS*

Answer: b [Reason:] If the source Zs is complex, then the condition for the maximum power to be transferred is ZL=ZS* that is load impedance is complex conjugate of source impedance.

7. If ZS=RS+jXS, ZL=RL, then condition for maximum power to be transferred is?
a) RL=|ZS|
b) RL=ZS
c) RL=-|ZS|
d) RL=-ZS

Answer: a [Reason:] If ZS=RS+jXS, ZL=RL, then condition for maximum power to be transferred is RL=|ZS| that is maximum power is transferred when the load resistance is equal to the magnitude of the source impedance.

8. Find the load resistance so that the load draws maximum power.
a) 6
b) 7
c) 8
d) 9

Answer: d [Reason:] The condition for the load to draw maximum power is by open circuiting terminals a and b and the load resistance is R=(10×6)/(10+6)+(15×8)/(15+8)=8.96Ω≅9Ω.

9. Find the maximum power (mW) that is delivered by the source in the circuit shown in the question 8.
a) 50
b) 51
c) 52
d) 53