AC Fundamentals MCQ [Free PDF] – 8 Objective Questions with Answers

In sinusoidal steady state, complex power combines real and reactive power as S=P+jQ. Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current. Key relation: S=P+jQ; |S|=√(P²+Q²); PF=P/|S|=cosφ.

Exam focus: Draw the power triangle before choosing a power-factor relation. Common trap: Do not confuse P/Q with power factor.

For an ideal square wave, the magnitude is constant throughout each half-cycle. Therefore peak value = rms value = average rectified value, making both peak factor and form factor equal to 1. Hence the two factors are equal for a square wave.

Frequency means cycles per second. At 100 Hz, the waveform completes 100 cycles each second; in 2 s it completes 100×2 = 200 cycles.

Peak factor (crest factor) is V_peak/V_rms. For a half-wave rectified sine, V_rms=V_m/2, so peak factor=2, which exceeds sine (√2), triangular (√3) and square (1).

RMS value is defined as the DC value that would produce the same heating effect in a given resistance over the same time. That is why RMS—not average or peak—is used for AC equipment voltage/current ratings.

The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V. The full-cycle average of a sine wave is zero. Key relation: Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.

Exam focus: Check whether the question asks full-cycle average or rectified average. Common trap: Using the half-cycle average as the full-cycle average is a common error.

For a sine wave x(t)=Xm sinωt, the RMS value is Xm/√2. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. Key relation: Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.

Exam focus: Check whether the question asks full-cycle average or rectified average. Common trap: Using the half-cycle average as the full-cycle average is a common error.

Peak factor directly relates the maximum (peak) value of an AC waveform to its RMS value. By definition, Peak factor = V_peak / V_rms, so V_peak = Peak factor × V_rms. For a sine wave the peak factor is √2.