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Right option is (C) increase the FIELD energy at constant currents

Best explanation: Te = ∂Wfld(is,ir,θr)/∂θr = ∂Wfld^1(is,ir,θr)/∂θr

fe = ∂Wfld(is,ir,x)/∂x = ∂Wfld^1(is,ir,x)/∂x

The POSITIVE sign in the formula indicates that force/torque acts in a DIRECTION as to tend to increase both field energy and co-energy.

The CORRECT answer is (d) any of the stator or rotor currents ACTING alone

For explanation I would say: EQUATION for magnetic TORQUE is Te=1/2is^2dLs/dθr+1/2ir^2dLr/dθr+isirdMsr/dθr, if ir=0, Te=1/2is^2dLs/dθr and if is=0, then Te = 1/2ir^2dLr/dθr, and these EQUATIONS for torque are called reluctance torques.

Right choice is (a) φm and 1.5φm, both ROTATING

Easy explanation: In a 2 phase and 3 phase AC machine, rotating MMF is PRODUCED with MAGNITUDES of φm and 3/2φm.

The correct OPTION is (d) Varying speed and a speed fluctuating around the SYNCHRONOUS speed

Best EXPLANATION: With one supply PHASE disconnected, a ROTATING MMF wave of varying amplitude is produced, but at a speed fluctuating around the synchronous speed.

Correct choice is (c) Equal to the space angle displacement between WINDING AXIS

For explanation I would SAY: If the time angle displacement between currents and space angle displacement between winding axis are not equal, the MAGNITUDE of resultant MMF wave is always zero.

The correct option is (b) DIRECTION reverses, AMPLITUDE unaltered

The explanation is: The direction of rotating MMF wave is REVERSED, THOUGH its amplitude remains unaltered.

The correct CHOICE is (a) MMF wave at any moment is sinusoidally distributed in space

Explanation: The space angle α means that MMF wave at any moment is sinusoidally distributed in space ALONG the air-gap PERIPHERY.

Correct option is (d) All of the mentioned

To ELABORATE: It is the decomposition of the MMF of a single phase WINDING into two counter ROTATING MMF waves, but are not actually produced and only one stationary MMF wave pulsating ALONG its magnetic AXIS is produced.

Right option is (d) 6k+1 and 6K-1 HARMONICS, where K is an integer

For EXPLANATION: Space harmonics of the order 3,9,15,… i.e, triplen harmonics are absent.

Correct choice is (b) Constant amplitude and ROTATES along F1

Explanation: Space harmonics of the order of 6K-1(5,11,17,…) have their constant amplitude equal to 1/(6K-1)F1 and ROTATE in the direction of FUNDAMENTAL component F1 at a speed of 1/(6K+1) of the fundamental synchronous speed.

Right OPTION is (b) Constant amplitude and rotates ALONG F1

Easiest explanation: Space harmonics of the order of 6K+1(7,13,19,…) have their constant amplitude equal to 1/(6K+1)F1 and ROTATE in the direction of fundamental component F1 at a SPEED of 1/(6K+1) of the fundamental synchronous speed.

The correct answer is (C) Nph and I

Best explanation: FR = 3/(2FM) = 3/(2 4√2/(ΠKw NphI/P)

whereNph = series turns per phase and I = RMS current.

Correct option is (B) Remains CONSTANT

Best explanation: FR = 3/(2Fm) (for a 3 PHASE machine). A constant amplitude rotating MMF or rotating field is PRODUCED in the air gap of a THREE phase machine.

Right option is (C) Mechanical rotation of either PERMANENT magnets or DC excited field poles, at SYNCHRONOUS speed

Easiest explanation: The speed at which rotating magnetic field revolves is called the synchronous speed and this effect is equivalent to mechanical rotation of permanent magnets or DC excited field poles.

Correct choice is (c) It is not a rotating MMF WAVE but its amplitude MERELY pulsates

For explanation I WOULD say: It should be remembered that individual phase MMF is not a rotating MMF wave, its amplitude merely pulsates or ALTERNATES along its own phase axis.

The correct ANSWER is (a) Be reversed

Easy explanation: A reversal of the phase SEQUENCE of SUPPLY currents will reverse the DIRECTION of rotation of the resultant MMF WAVE.

The CORRECT option is (a) The AXIS of that phase which carries the MAXIMUM current at that INSTANT

The explanation: The resultant MMF FR = 3/(2Fm) is directed along the axis of that phase, which carries the maximum current at that instant.

Correct option is (c) (m/2)Fm

To explain I would SAY: In general m phase current FLOWING in m phase WINDING results in rotating MMF wave of constant AMPLITUDE, equal to m/(2FM).

The CORRECT choice is (B) SYNCHRONOUS SPEED

To elaborate: Rotating field speed (Ns) = 120f/(P r.p.m) = synchronous speed.

Correct option is (C) for both cylindrical and salient pole rotor

Best explanation: It does not make any difference whether the FIELD WINDING is on cylindrical pole structure or salient pole structure.

Right OPTION is (C) Bplr

To elaborate: TOTAL FLUX per pole = 4/PBplr, SINCE P=4, Φ=Bplr.

The CORRECT choice is (a) 180 electrical DEGREES

To EXPLAIN I WOULD say: A coil, with two coil-sides 180 electrical space degrees apart (or ONE pole-pitch apart), is called a full pitch coil.

The correct OPTION is (b) two CONDUCTORS

To elaborate: ONE turn CONSISTS of two conductors, and one coil is made up of two coil-sides.

Right choice is (b) TWO COIL SIDES

For explanation: ONE coil is MADE up of two coil sides.

The correct answer is (B) COIL sides

The explanation is: The EMF is GENERATED in the ACTIVE lengths only, and these active lengths are called the coil-sides of a coil.

The correct OPTION is (a) = 180° electrical

For EXPLANATION I would SAY: Pole PITCH is ALWAYS expressed in electrical degrees, rather than in mechanical degrees.

pole pitch = 180 electrical degrees or π electrical radians.

Right choice is (b) 0.157H

Easy EXPLANATION: Reluctance Rl=2g/μ0A and COIL Inductance L=N^2/Rl = N^2μ0A/2g = (1000)^2(4π∗10^-7)(0.05)^2/(2∗0.01) = 0.15708H.

The correct answer is (d) θelec = P/2 θmech

Explanation: For a P-pole MACHINE, P/2 cycles of EMF will be generated in ONE REVOLUTION, and thus θelec = P/2 θmech.

Correct ANSWER is (d) their CONSTRUCTION details are different

The EXPLANATION: Though AC and DC machine have same operating fundamental PRINCIPLES, their construction details differ.

Right CHOICE is (c) applicable to both AC and DC machines

For explanation I would say: Basic torque and EMF expressions are same for both AC and DC machines as the fundamental PRINCIPLES underlying the operation of AC and DC machines are same.

Right choice is (b) stator FIELD axis and rotor field axis

To elaborate: The angle between the stator field axis and rotor field axis is CALLED as TORQUE angle.

Correct option is (c) equal to the stator poles

The EXPLANATION: If the rotor poles are not equal to the stator poles, the NET electromagnetic torque will be zero as the force of ATTRACTION will be cancelled by the force of REPULSION.

The correct choice is (b) ZERO or no torque is developed

Easiest EXPLANATION: In a MACHINE with 2 stator poles and 4 rotor poles spaced equally, the force of ATTRACTION will be cancelled due to the force of repulsion, and hence the net electromagnetic torque will be zero.

The correct choice is (C) Te ∝ (stator field strength)(rotor field strength)sinδ

The explanation: The tendency of TWO fields (stator field and rotor field), to align themselves in the same direction, is CALLED INTERACTION torque, and it ALSO depends on the torque angle & delta;.

The correct choice is (b) 1/8π∗10^3 N

The best I can EXPLAIN: When electric field is applied, the plates MOVE towards each other because of force of attraction by a distance X ⇒ C = ε0A/(g-x)

Wfld(q,x) = 1/2 q^2/C = 1/2 q^2(g-x)/Aε0

fe = -∂Wfld(q,x)/∂x = 1/2q^2x/Aε0

We KNOW, q = DA = ε0EA and ε0 = 10^-9/36Π

fe = 1/2 E^2ε0A = 1/2∗(3∗10^6)^2∗10^-9/36Π∗1 = 1/8π∗10^3 N

The CORRECT choice is (d) 44.3 nJ

For EXPLANATION: WFLD = 1/2 q^2/C(X)

C(x) = ε0A/x = 8.85∗10^-12∗100∗(10^-3)^2/0.1∗10^-3 = 8.85∗10^-12 F

Wfld = 1/2∗Cv = 1/2∗100^2∗8.85∗10^-12 = 44.3nJ

Correct choice is (C) reduce to half

The explanation: A2=2A1, x2=2x1, v2=v1, fe2=1/2v^2dC(x)/dx2, C2=ε0A2/x2 ⇒ dC2/dx2 = -ε0A2/x2^2

dC2/dx2 = -2ε0A1/4x1^2 = -ε0A1/2x1^2 ⇒ f&e2 = -1/2v1^2ε0A1/2x1^2 = -1/2(FE1)

⇒ FORCE REDUCES to half.

The correct option is (a) -233.88N-m

Best EXPLANATION: For θr=60°; Ls, Lr, Msr and their DERIVATIVES with RESPECT to θr have the FOLLOWING values:

Ls=0.50H, Lr=0.60H, Msr=0.40H, dLs/dθr=-0.3464, dLr/dθr=-0.52, dMsr/dθr=-0.693

Substituting the numerical values in TE = 1/2is^2dLs/dθr+1/2ir^2dLr/dθr+isrdMsr/dθr = -233.88N-m.

The correct answer is (a) 1/2 IfImMmaxsinδ

Best explanation: The torque developed by the INTERACTION of both stator and rotor MAGNETIC FIELDS is the electromagnetic/interaction torque.

The CORRECT CHOICE is (d) Te(AV) = 1/8 Im^2(Ld-Lq)sin2δ

To elaborate: Te(av) = 1/8 Im^2(Ld-Lq)sin2δ+1/2 IfImMmaxsinδ

If field current If is REDUCED to ZERO, the reluctance torqueTe(av) = 1/8 Im^2(Ld-Lq)sin2δ.

Correct option is (c) constant at EVERY INSTANT of time

To explain: TE = IfImMmaxsinδ

We can OBSERVE that it REMAINS constant at every instant of time.