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The CORRECT option is (d) 0.707

The BEST I can EXPLAIN: We know that the rms value is 1/√2 times the MAXIMUM value, hence the rms value is 0.707 times the maximum value.

The correct OPTION is (C) 300

To EXPLAIN: We know that f=p*n

f=15kHz=15000Hz, p=50

15000=50*n => n=15000/50=300.

Right choice is (a) Magnitude of the QUANTITY

The explanation is: The LENGTH of the PHASOR ARROW REPRESENTS the magnitude of the quantity, whereas the angle between the phasor and the reference represents the phase angle.

The correct choice is (b) INSTANTANEOUS value

For explanation: Instantaneous value is the value of the waveform at that INSTANT. HENCE the value of a given waveform at any instant time is termed as instantaneous value.

The correct answer is (c) 5+11j V

The explanation: The total voltage in the circuit is the sum of the TWO VOLTAGES where we add the REAL parts and IMAGINARY parts separately.

Therefore, Vtotal= 5+11j V.

Right choice is (b) Average CURRENT

Easiest explanation: The average value of the current is the sum of all the CURRENTS DIVIDED by the NUMBER of currents.

The correct answer is (b) Less than

Best EXPLANATION: The average VALUE of current is the SUM of all the currents divided by the NUMBER of currents whereas RMS current is obtained by squaring all the current values, finding the average and then finding the SQUARE root. Hence RMS current is greater than average current.

Right answer is (c) 18V

Best EXPLANATION: Vp-p=2Vp

Substituting the VALUES from the QUESTION, we GET Vp-p= 18V.

Correct answer is (C) e=Blvsin(θ)

EASY EXPLANATION: The correct expression for alternating emf generated is e=Blvsin(θ). Where B stands for MAGNETIC field density, l is the length of each of the parallel sides V is the velocity with which the conductor is moved and θ is the angle between the velocity and the length.

Correct option is (c) 13.23 A

The explanation: Resultant CURRENT can be FOUND using I^2 = I1^2 + I2^2 + 2I1I2 cosθ

Substituting the values, we get I=13.23 A.

Right option is (a) RECTANGULAR

To explain I WOULD say: For addition and SUBTRACTION of phasors, we use the rectangular form because in the rectangular form we can only ADD the real part and the complex part separately to get the total value.

Correct answer is (a) 10/π A

To explain I would say: We KNOW, the value of the average CURRENT = value of MAX current *√2 /π

Substituting the value of max current we get, rms current = 10/π A.

The correct answer is (a) RMS current

Explanation: RMS current is also known as the effective current. RMS STANDS for ROOT MEAN SQUARE. This value of current is OBTAINED by squaring all the current values, finding the average and then finding the square root.

The correct answer is (b) Lagging

To explain I would say: The sine WAVE is said to lag because it passes though ZERO following the other, hence it crosses zero after the first wave, THEREFORE it is said to lag.

Correct option is (b) AVERAGE current

Explanation: The average VALUE of current is the sum of all the CURRENTS DIVIDED by the number of currents. Hence it can also be found by dividing the area enclosed by the half cycle by the length of the base of the half cycle.

The correct answer is (d) 5V

The EXPLANATION is: Vp-p=2Vp

Substituting the VALUES from the QUESTION, we GET Vp=5V.

Right answer is (a) WAVEFORM

To EXPLAIN I would SAY: The variation of a quantity, which is voltage or current in this CASE, shown on a graph with the x-axis as time is known as a waveform.

Right answer is (b) Irms / IAV

To EXPLAIN: The correct expression for form FACTOR is Irms/Iav where Irms is the rms value of the current and Iav is the AVERAGE current.

Correct OPTION is (C) REMAINS constant

Explanation: When phasors are drawn representing the MAXIMUM values instead of the rms value, the shape of the diagram remains UNALTERED and hence the phase angle remains the same.

The CORRECT choice is (B) 0

Best explanation: Average of SINE or cosine over a PERIOD is zero so, average value of CURRENT over full cycle is zero.

Right answer is (a) 0.67Im

The BEST EXPLANATION: Average CURRENT = ∫0^πidθ/π = ∫0^πImsinθ dθ/π = 2Im/π =0.67 IM.

The correct choice is (B) 5 A

Easiest explanation: We KNOW, value of RMS current =value of max current/√2

Substituting the value of max current we GET, rms current = 5A.

The correct CHOICE is (a) INCREASES

Easy explanation: We know that:

f=p*N, THEREFORE, as n increases, f also increases.

Hence FREQUENCY increases if number of revolutions increases.

The correct choice is (a) 30 DEGREES

Explanation: The value of the phase ANGLE is the value at which the phasor stops or freezes. Here, it freezes at 30 DEGREE, HENCE the phase angle is 30 degrees.

Right answer is (d) 8+10j A

The explanation: The total current in the circuit is the sum of the TWO currents where we add the REAL parts and IMAGINARY parts separately.

Therefore, Itotal= 8+10j A.

Correct option is (a) π/2

Easy explanation: For SINUSOIDAL current, Irms=Im/√2

Iav=√2 Im/π

So, form FACTOR = Irms/Iav = π/2.

Right option is (a) Increases EMF

The EXPLANATION is: In an A.C. generator, the emf increases as the number of turns in the coil increases because the emf is directly PROPORTIONAL to the number of turns.

The correct option is (c) Both PEAK and crest factor

The explanation: Peak and crest factor both mean the same THING. Hence the peak VALUE divided by the RMS value gives us the peak or crest factor.

Right option is (a) 150V

For EXPLANATION: We know that: emax=Bvl

Substituting the values from the GIVEN QUESTION, we get e=150V.

Correct answer is (b) 90^0

Easy explanation: The VALUE of θ should be 90^0 in ORDER to GET maximum EMF because E = Blvsin(θ) and sin is maximum when θ is 90^0.

Right ANSWER is (c) 50HZ

To ELABORATE: For a two POLE machine, p=1.

f=pn = 1*50 = 50Hz.

Right ANSWER is (c) 50

The EXPLANATION is: We KNOW that f=p*n

f=15kHz=15000Hz, n=300

15000=p*300 =>p=15000/300=50.

Right choice is (c) Vp-p=2Vp

The explanation is: The maximum VARIATION between the maximum positive INSTANTANEOUS value and the maximum NEGATIVE instantaneous value is the peak-to-peak value. For a SINUSOIDAL waveform, it is twice the peak value. HENCE Vp-p=2Vp.

Right choice is (b) Frequency

For explanation I WOULD say: The number of cycles that occur in ONE second is KNOWN as the frequency. It is the reciprocal of the TIME PERIOD.

The CORRECT option is (a) RMS value

The explanation is: AMMETERS and VOLTMETERS are calibrated to READ the rms value, hence the phasors are drawn representing the rms VALUES.

Correct answer is (C) Conductors MOVE past north and south poles

To ELABORATE: The WAVEFORM of the e.m.f. generated in an a.c. generator undergoes one complete cycle of variation when the conductors move past an N and an S pole.

Correct CHOICE is (B) PEAK to peak value

Explanation: The MAXIMUM variation between the maximum POSITIVE instantaneous value and the maximum negative instantaneous value is the peak-to-peak value.

Correct ANSWER is (b) Phase angle

The best explanation: The TIME axis while measuring an AC SINUSOIDAL voltage or current REPRESENTS the phase angle when converting it to a phasor.