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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Average value of current is given by
Im
0.5Im
0.707Im
0.637Im
0.637Im
Quick Summary: The average value of a sinusoidal alternating current over a half-cycle is defined as the arithmetic mean of all instantaneous values. For a symmetrical sinusoidal waveform, this is calculated as $\frac{2I_m}{\pi}$, which evaluates to approximately $0.637I_m$.
The average value of a sinusoidal alternating current over a half-cycle is defined as the arithmetic mean of all instantaneous values. For a symmetrical sinusoidal waveform, this is calculated as π2Im, which evaluates to approximately 0.637Im.
Iavg=π2Im — Average value for a half-cycle
Irms=2Im≈0.707Im — Root Mean Square value
The average value is derived by integrating the instantaneous current i=Imsin(ωt) over the interval from 0 to π and dividing by the interval duration π. Mathematically, Iavg=π1∫0πImsin(θ)dθ=πIm[−cos(θ)]0°π=π2Im≈0.637Im. Over a full cycle, the average value of a pure sinusoidal wave is zero due to the cancellation of the positive and negative half-cycles.
The average value is strictly defined for a half-cycle in AC circuits.
Form factor is defined as the ratio of RMS value to Average value, which is ≈1.11 for a sine wave.
The average value over a complete period for a symmetrical AC signal is zero.
Useful in calculating DC equivalent output in half-wave and full-wave rectifiers.
Simplifies analysis of pulsating DC components in electrical machines.
Not representative of the actual power-delivering capability of the AC signal.
Mathematically zero over a full cycle, requiring half-cycle rectification for meaningful measurement.
Moving coil (PMMC) instrument calibration.
Design and analysis of rectifier circuits.
Option B (0.5Im) is incorrect and holds no standard physical significance for sine waves.
Option C (0.707Im) refers to the RMS (Root Mean Square) value, not the average value.
D is correct — The average value of a sinusoidal current over one half-cycle is mathematically derived as 2Im/π, resulting in 0.637Im.
Always distinguish between Average and RMS values; recall that Form Factor = RMS/Average = 1.11 for sinusoidal signals.