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## Network Theory MCQ Set 1

1. The power generated by a machine increases _____________ percent from single phase to two phase.
a) 40.4
b) 41.4
c) 42.4
d) 43.4

Answer: b [Reason:] In an ac system it is possible to connect two or more number of individual circuits to a common poly phase source. The power generated by machine increases 41.4 percent from single phase to two phase. So, percentage increase = 41.4%.

2. The percentage of power increased from single phase to three phase is?
a) 50
b) 100
c) 150
d) 200

Answer: a [Reason:] The percentage of power increased from single phase to three phase is 50. So, percentage increase = 50%. Beyond three phase the maximum possible increase is only seven percent but the complications are many.

3. When the power factor is __________ the power becomes zero 100 times a second in a 50Hz supply.
a) 0
b) 1
c) 2
d) 3

Answer: b [Reason:] The power in a single phase circuit is pulsating. When the power factor is one, the power becomes zero 100 times a second in a 50Hz supply. Therefore single phase motors have a pulsating torque.

4. Which motors are called self-starting motors?
a) single phase
b) two phase
c) three phase
d) four phase

Answer: c [Reason:] Three phase motors are more easily started than single phase motors. Three phase motors are called self-starting motors. Single phase or two phase or four phase motors are not called self-starting motors.

5. In three phase system, the three voltages (currents) differ in phase by __________electrical degrees from each other in a particular sequence.
a) 30
b) 60
c) 90
d) 120

Answer: d [Reason:] In general a three phase system of voltages is merely a combination of three single phase systems of voltages. In three phase system, the three voltages (currents) differ in phase by 120⁰ from each other in a particular sequence.

6. In a two phase generator, the armature has two distinct windings that are displaced __________ apart.
a) 45⁰
b) 90⁰
c) 135⁰
d) 180⁰

Answer: b [Reason:] Single phase voltages and currents are generated by single phase generators and the armature of such generator has only one winding or one set of coils. In a two phase generator, the armature has two distinct windings that are displaced 90⁰ apart. θ= 90⁰.

7. In three phase system at any given instant, the algebraic sum of three voltages must be?
a) 0
b) 1
c) 2
d) 3

Answer: a [Reason:] For three phase alternator the three voltages are of same magnitude and frequency. In three phase system at any given instant, the algebraic sum of three voltages must be zero. Algebraic sum of three voltages = 0.

8. Phase sequence depends on the?
a) field
b) rotation of the field
c) armature
d) rotation of the armature

Answer: b [Reason:] The sequence of voltages in the three phases undergo changes one after the other abd this is called phase sequence. Phase sequence depends on the rotation of the field not on rotation of armature or on field or on armature.

9. If RR, YY and BB constitutes three phase sequence if VRR = Vmsinωt its corresponding field magnets are in clockwise direction, then VYY =?
a) Vmsinωt
b) Vmsin(ωt+120⁰)
c) Vmsin(ωt-120⁰)
d) Vmsin(ωt-240⁰)

Answer: c [Reason:] If the field system is rotated in the anticlockwise direction, then the sequence of voltages in the three phases are in order RBY. The value of VYY is VYY = Vmsin(ωt-120⁰).

10. The value of VBB in the question 9 is?
a) Vmsin(ωt-240⁰)
b) Vmsin(ωt-120⁰)
c) Vmsin(ωt+240⁰)
d) Vmsinωt

Answer: a [Reason:] The value of VBB is VBB = Vmsin(ωt-240⁰). There are only two possible phase sequences; they are RBY and RYB.

## Network Theory MCQ Set 2

1. The driving point function is the ratio of polynomials in s. Polynomials are obtained from the __________ of the elements and their combinations.
a) transform voltage
b) transform current
c) transform impedance

Answer: c [Reason:] The driving point function is the ratio of polynomials in s. Polynomials are obtained from the transform impedance of the elements and their combinations and if the zeros and poles are not repeated then the poles or zeros are said to be distinct or simple.

2. The pole is that finite value of S for which N (S) becomes __________
a) 0
b) 1
c) 2
d) ∞

Answer: d [Reason:] The quantities P1, P2 … Pm are called poles of N (S) if N (S) = ∞ at those points. The pole is that finite value of S for which N (S) becomes infinity.

3. A function N (S) is said to have a pole (or zero) at infinity, if the function N (1/S) has a pole (or zero) at S = ?
a) ∞
b) 2
c) 0
d) 1

Answer: c [Reason:] A function N (S) is said to have a pole (or zero) at infinity, if the function N (1/S) has a pole (or zero) at S = infinity. A zero or pole is said to be of multiplicity ‘r’ if (S-Z)r or(S-P)r is a factor of P(s) or Q(s).

4. The number of zeros including zeros at infinity is __________ the number of poles including poles at infinity.
a) greater than
b) equal to
c) less than
d) greater than or equal to

Answer: b [Reason:] The number of zeros including zeros at infinity is equal to the number of poles including poles at infinity and it cannot be greater than or less than the number of poles including poles at infinity.

5. The poles of driving point impedance are those frequencies corresponding to ___________ conditions?
a) short circuit
b) voltage source
c) open circuit
d) current source

Answer: c [Reason:] A zero of N(s) is a zero of V(s),it signifies a short circuit. Similarly a pole of Z(s) is a zero of I(s). The poles of driving point impedance are those frequencies corresponding to open circuit conditions.

6. The zeros of driving point impedance are those frequencies corresponding to ___________ conditions?
a) current source
b) open circuit
c) voltage source
d) short circuit

Answer: d [Reason:] The zeros of driving point impedance are those frequencies corresponding to short circuit conditions as pole of Z(s) is a zero of I(s) and zero of N(s) is a zero of V(s),it signifies a short circuit.

7. In the driving point admittance function, a zero of Y (s) means a _______of I (S).
a) 1
b) 2
c) 3
d) zero

Answer: d [Reason:] In the driving point admittance function, a zero of Y (s) means a zero of I (S) i.e., the open circuit condition as the driving point admittance function is the ratio of I(s) to V(s).

8. In the driving point admittance function, a pole of Y (s) means a _______ of V (S).
a) zero
b) 1
c) 2
d) 3

Answer: a [Reason:] The driving point admittance function Y(s) = I(s)/V(s). In the driving point admittance function, a pole of Y (s) means a zero of V (S) i.e., the short circuit condition.

9. The real part of all zeros and poles must be?
a) positive or zero
b) negative or zero
c) positive
d) negative

Answer: b [Reason:] The real part of all zeros and poles must be negative or zero. But the poles or zeros should not be positive because if they are positive, then they will lie in the right-half of the s-plane.

10. Poles or zeros lying on the jω axis must be?
a) complex
b) at least one complex pole
c) at least one complex zero
d) simple

Answer: d [Reason:] Poles or zeros lying on the jω axis must be simple because on jω axis the imaginary part of poles or zeros will be zero.

## Network Theory MCQ Set 3

1. The coefficients of numerator polynomial and the denominator polynomial in a transfer function must be?
a) real
b) complex
c) at least one real coefficient
d) at least one complex coefficient

Answer: a [Reason:] The coefficients of P(s), the numerator polynomial and of Q(s), the denominator polynomial in a transfer function must be real. Therefore all poles and zeros if complex must occur in conjugate pairs.

2. In a transfer function, the degree of numerator polynomial is ___________ than the degree of the denominator polynomial.
a) greater than
b) less than
c) equal to
d) less than or equal to

Answer: d [Reason:] In a transfer function, the degree of numerator polynomial is less than or equal to than the degree of the denominator polynomial. And the degree of the numerator polynomial of Z21(s) or Y21(s) is less than or equal to the degree of the denominator polynomial plus one.

3. The real parts of all poles and zeros in a driving point function must be?
a) zero
b) negative
c) zero or negative
d) positive

Answer: c [Reason:] The real parts of all poles and zeros in a driving point function must be zero or negative but should not be positive and the complex or imaginary poles and zeros must occur in conjugate pairs.

4. If the real part of driving point function is zero, then the pole and zero must be?
a) complex
b) simple
c) one complex pole
d) one complex zero

Answer: b [Reason:] If the real part of driving point function is zero, then the pole and zero must be simple but should not contain any complex pole or complex zero.

5. The degree of the numerator polynomial and denominator polynomial in a driving point function may differ by?
a) 0
b) 1
c) 0 or 1
d) 2

Answer: c [Reason:] The degree of numerator polynomial and denominator polynomial in a driving point function may differ by zero or one. And the polynomials P(s) and Q(s) may not have any missing terms between the highest and lowest degrees unless all even or odd terms are missing.

6. The lowest degree in numerator polynomial and denominator polynomial in a driving point function may differ by at most __________
a) 0
b) 1
c) 2
d) 3

Answer: b [Reason:] The lowest degree in numerator polynomial and denominator polynomial in a driving point function may differ by at most one and the coefficients in the polynomials P(s) and Q(s) of network function must be real and positive.

7. The coefficients in the denominator polynomial of the transfer function must be?
a) positive
b) negative
c) positive or zero
d) negative or zero

Answer: a [Reason:] The coefficients in the denominator polynomial of the transfer function must be positive but should not be negative and the coefficients in the polynomials P(s) and Q(s) of transfer function must be real.

8. The coefficients in the numerator polynomial of the transfer function may be?
a) must be negative
b) must be positive
c) may be positive
d) may be negative

Answer: d [Reason:] The coefficients in the numerator polynomial of the transfer function may be negative and the complex or imaginary poles and zeros must occur in conjugate pairs.

9. The denominator polynomial in a transfer function may not have any missing terms between the highest and the lowest degree, unless?
a) all odd terms are missing
b) all even terms are missing
c) all even or odd terms are missing
d) all even and odd terms are missing

Answer: c [Reason:] The denominator polynomial in a transfer function may not have any missing terms between the highest and the lowest degree, unless all even or odd terms are missing and the polynomial P(s) may have missing terms between the lowest and the highest degree.

10. The degree of numerator polynomial in a transfer function may be as small as _________ independent of the degree of the denominator polynomial.
a) 1
b) 2
c) 0
d) 3

Answer: c [Reason:] The degree of numerator polynomial in a transfer function may be as small as zero, independent of the degree of the denominator polynomial and for the voltage transfer ratio and the current transfer ratio, the maximum degree of P(s) must be equal to the degree of Q(s).

## Network Theory MCQ Set 4

1. In a three phase alternator, there are __________ independent phase windings or coils.
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] In a three phase alternator, there are 3 independent phase windings or coils. So, 3 independent phase windings or coils. The end connections of the three sets of the coils may be brought out of the machine to form three separate single phase sources to feed three individual circuits.

2. Each coil in three phase alternator has ________________ number of terminals.
a) 2
b) 4
c) 6
d) 8

Answer: a [Reason:] Each coil in three phase alternator has 2 number of terminals, viz. start and finish. So, 2 number of terminals. the coils are inter connected to form a wye or delta connected three phase system to achieve economy and reduce the number of conductors and thereby the complexity of the circuit.

3. In wye or star connection, ______________ of the three phases are joined together within the alternator.
a) similar ends
b) opposite ends
c) one similar end, two opposite ends
d) one opposite end, two opposite ends

Answer: a [Reason:] In wye or star connection, similar ends of the three phases are joined together within the alternator. The common terminal so formed is referred to as the neutral point or neutral terminal.

4. The voltage between __________ and ___________ is called phase voltage.
a) line and line
b) line and reference
c) neutral point and reference
d) line and neutral point

Answer: d [Reason:] In a three phase four wire star connected system, the terminals R, Y and B are called the line terminals of the source. The voltage between line and neutral point is called phase voltage. And the voltage between line and line is called line voltage.

5. The voltage between ______________ is called line voltage.
a) line and neutral point
b) line and reference
c) line and line
d) neutral point and reference

Answer: c [Reason:] The voltage between line and line is called line voltage. And the voltage between line and neutral point is called phase voltage. The currents flowing through the phases are called the phase currents, while those flowing in the lines are called the line currents.

6. Figure below represents three phases of an alternator. The phase voltage for the star connection among the options given below is?

a) VRY
b) VRN
c) VYB
d) VBR

Answer: b [Reason:] If the neutral wire is not available for external connection, the system is called a three phase,three wire star connected system. Phase voltage = VRN. And VRY, VYB and VBR are not phase voltages.

7. In the figure shown above, what will be the line voltage?
a) VBR
b) VBN
c) VRN
d) VYN

Answer: a [Reason:] The star connected system formed will supply equal line voltages displaced 120 from one another and acting simultaneously in the cicruit like three independent single phase sources in the same frame of a three phase alternator. Line voltage = VBR. And VRN , VYN and VBN are not line voltages.

8. In the Delta or Mesh connection, there will be __________ number of common terminals.
a) 1
b) 2
c) 3
d) 0

Answer: d [Reason:] The three line conductors are taken from the three junctions of the mesh or delta connection to feed the three phase load. This constitutes a three phase, three wire, delta connected system. In the Delta or Mesh connection, there will be zero number of common terminals. Number of common terminals = 0.

9. The relation between line voltage and phase voltage in Delta or Mesh connection is?
a) Vphase > Vline
b) Vphase < Vline
c) Vphase = Vline
d) Vphase >= Vline

Answer: c [Reason:] When the sources are connected in delta, loads can be connected only across the three line terminal. The relation between line voltage and phase voltage in Delta or Mesh connection is Vphase = Vline.

10. Which of the following voltage is a phase voltage in delta connection?
a) VRN
b) VBR
c) VYN
d) VBN

Answer: b [Reason:] A balanced three phase source is one in which the three individual sources have equal magnitude with 120 phase differences. VBR is a phase voltage in delta connection. And VRN , VYN and VBNare not phase voltages.

## Network Theory MCQ Set 5

1. The reactive power equation (Pr) is?
a) Ieff2 (ωL)sin2(ωt+θ)
b) Ieff2 (ωL)cos2(ωt+θ)
c) Ieff2 (ωL)sin(ωt+θ)
d) Ieff2 (ωL)cos(ωt+θ)

Answer: a [Reason:] If we consider a circuit consisting of a pure inductor, the power in the inductor is reactive power and the reactive power equation (Pr) is Pr =Ieff2 (ωL)sin2(ωt+θ).

2. Reactive power is expressed in?
a) Watts (W)
b) Volt Amperes Reactive (VAR)
c) Volt Ampere (VA)
d) No units

Answer: b [Reason:] Reactive power is expressed in Volt Amperes Reactive (VAR) and power is expressed in watts and apparent power is expressed in Volt Ampere (VA).

3. The expression of reactive power (Pr) is?
a) VeffImsinθ
b) VmImsinθ
c) VeffIeffsinθ
d) VmIeffsinθ

Answer: c [Reason:] The expression of reactive power (Pr) is VeffIeffsinθ Volt Amperes Reactive (VAR). Reactive power =VeffIeffsinθ Volt Amperes Reactive (VAR).

4. The power factor is the ratio of ________ power to the ______ power.
a) average, apparent
b) apparent, reactive
c) reactive, average
d) apparent, average

Answer: a [Reason:] The power factor is the ratio of average power to the apparent power. Power factor =(average power)/(apparent power).

5. The expression of true power (Ptrue) is?
a) Pasinθ
b) Pacosθ
c) Patanθ
d) Pasecθ

Answer: b [Reason:] True power is the product of the apparent power and cosθ. The expression of true power (Ptrue) is Pacosθ. True power = Pacosθ.

6. The average power (Pavg) is expressed as?
a) Pasecθ
b) Patanθ
c) Pacosθ
d) Pasinθ

Answer: c [Reason:] The average power is the product of the apparent power and cosθ. The average power (Pavg) is expressed as Pacosθ. Average power = Pacosθ.

7. The equation of reactive power is?
a) Pacosθ
b) Pasecθ
c) Pasinθ
d) Patanθ

Answer: c [Reason:] The reactive power is the product of the apparent power and sinθ. The equation of reactive power is Pasinθ. Reactive power = Pasinθ.

8. A sinusoidal voltage v = 50sinωt is applied to a series RL circuit. The current in the circuit is given by I = 25sin (ωt-53⁰). Determine the apparent power (VA).
a) 620
b) 625
c) 630
d) 635

Answer: c [Reason:] The expression of apparent power (VA) is Papp= VeffIeff = (Vm/√2)×(Im/√2). On substituting the values Vm = 50, Im =25, we get apparent power = (50×25)/2 = 625VA.

9. Find the power factor in the question 8.
a) 0.4
b) 0.5
c) 0.6
d) 0.7

Answer: c [Reason:] In sinusoidal sources the power factor is the cosine of the phase angle between the voltage and the current. The expression of power factor = cosθ = cos53⁰ = 0.6.

10. In the question 8 determine the average power.
a) 365
b) 370
c) 375
d) 380