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Average value of current is given by
ImтАЛ
0.5ImтАЛ
0.707ImтАЛ
0.637ImтАЛ
0.637ImтАЛ
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 ╧А2ImтАЛтАЛ, which evaluates to approximately 0.637ImтАЛ.
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 ╧А2ImтАЛтАЛ, which evaluates to approximately 0.637ImтАЛ.
IavgтАЛ=╧А2ImтАЛтАЛ тАФ Average value for a half-cycle
IrmsтАЛ=2тАЛImтАЛтАЛтЙИ0.707ImтАЛ тАФ Root Mean Square value
The average value is derived by integrating the instantaneous current i=ImтАЛsin(╧Йt) over the interval from 0 to ╧А and dividing by the interval duration ╧А. Mathematically, IavgтАЛ=╧А1тАЛтИл0╧АтАЛImтАЛsin(╬╕)d╬╕=╧АImтАЛтАЛ[тИТcos(╬╕)]0╧АтАЛ=╧А2ImтАЛтАЛтЙИ0.637ImтАЛ. 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 тЙИ1.11 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 тАФ The average value of a sinusoidal current over one half-cycle is mathematically derived as 2ImтАЛ/╧А, resulting in 0.637ImтАЛ.
Always distinguish between Average and RMS values; recall that Form Factor = RMS/Average = 1.11 for sinusoidal signals.