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Single phase AC power
Is constant
Pulsates around an average power at double frequency
Pulsates around the average value at the supply frequency
None of above
Pulsates around an average power at double frequency
In a single-phase AC circuit, the instantaneous power is the product of instantaneous voltage and current ┬╖ Because both quantities are sinusoidal and vary at the supply frequency, their product results in a power waveform that fluctuates at twice the supply frequency about an average value.
In a single-phase AC circuit, the instantaneous power is the product of instantaneous voltage and current ┬╖ Because both quantities are sinusoidal and vary at the supply frequency, their product results in a power waveform that fluctuates at twice the supply frequency about an average value.
p(t)=VIcos(╧Х)тИТVIcos(2╧ЙtтИТ╧Х) тАФ Instantaneous power in single phase
fpowerтАЛ=2├ЧfsupplyтАЛ тАФ Power pulsation frequency
Given v(t)=VmтАЛsin(╧Йt) and i(t)=ImтАЛsin(╧ЙtтИТ╧Х), the instantaneous power p(t)=v(t)i(t)=VmтАЛImтАЛsin(╧Йt)sin(╧ЙtтИТ╧Х). Using trigonometric identities, this simplifies to p(t)=VIcos(╧Х)тИТVIcos(2╧ЙtтИТ╧Х), where the first term is constant (average power) and the second term is a pulsating component oscillating at 2╧Й frequency.
Average power is constant, but instantaneous power is time-varying.
The pulsating component oscillates at double the supply frequency (2╧Й).
For a purely resistive load, the pulsating power hits zero twice per cycle.
This double frequency pulsation is a characteristic property of single-phase systems compared to balanced three-phase systems.
Simpler wiring and installation
Adequate for low power appliances
Constant power pulsation leads to vibrations in electrical machines
Requires larger capacitors for filtering in rectification
Domestic lighting
Small heating appliances
Single-phase motors for light loads
In a balanced three-phase system, the total instantaneous power is constant and does not pulsate.
Option A is incorrect because the instantaneous power is never constant in a single-phase AC circuit.
Option C is incorrect because the pulsation frequency is 2f, not f.
B is correct тАФ The instantaneous power in a single-phase AC circuit pulsates at twice the supply frequency due to the product of two sinusoidal waves of the same frequency.
Always remember that while single-phase systems have power pulsations at 2f, a balanced three-phase system provides constant power delivery, which is why industrial machines prefer three-phase supply.