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If the supply has frequency f Hz then what would be the frequency of intantaneous power?
f
x f
f / 2
f x f
x f
The instantaneous power in an AC circuit containing resistance and reactance oscillates at a frequency that is exactly double the supply frequency. This occurs because the product of voltage (v(t)=VmтАЛsin(╧Йt)) and current (i(t)=ImтАЛsin(╧ЙtтИТ╧Х)) generates a component containing the term sin(╧Йt)sin(╧ЙtтИТ╧Х), which expands into a term involving 2╧Йt.
The instantaneous power in an AC circuit containing resistance and reactance oscillates at a frequency that is exactly double the supply frequency. This occurs because the product of voltage (v(t)=VmтАЛsin(╧Йt)) and current (i(t)=ImтАЛsin(╧ЙtтИТ╧Х)) generates a component containing the term sin(╧Йt)sin(╧ЙtтИТ╧Х), which expands into a term involving 2╧Йt.
p(t)=VIcos(╧Х)тИТVIcos(2╧ЙtтИТ╧Х) тАФ Instantaneous power expression
fpтАЛ=2f тАФ Frequency of power relative to supply frequency
In an AC circuit, p(t)=v(t)cdoti(t). Using the trigonometric identity sin(A)sin(B)=21тАЛ[cos(AтИТB)тИТcos(A+B)], the product results in a constant term and a time-varying term that fluctuates at an angular frequency of 2╧Й. Since ╧Й=2╧Аf, the frequency of power becomes 2f, representing two power cycles for every one cycle of voltage/current.
The instantaneous power consists of a constant average component and an oscillating component.
The oscillating component frequency is 2f because of the product of two sinusoidal functions of frequency f.
In purely resistive circuits, the power never becomes negative but oscillates between 0 and 2VmтАЛImтАЛ at frequency 2f.
Useful for calculating instantaneous torque in electric motors.
Essential for analyzing vibration and ripple in power electronic converters.
AC motor torque ripple analysis
Power quality and harmonic analysis
Rectifier circuit design
The constant term represents the real (active) power, while the oscillating term represents the alternating power flow.
Option A is incorrect as it implies power frequency equals supply frequency. Option C is incorrect as it would imply power frequency is slower than voltage, which is physically impossible in linear AC systems.
B is correct тАФ The frequency of instantaneous power in an AC circuit is 2f, which is twice the supply frequency.
Always remember that whenever two signals of frequency f are multiplied, the resultant frequency is 2f due to product-to-sum trigonometric identities.