#### PG1995

##### Active Member

A capacitor stores its energy in form of electric field which results from static charges. In a pure capacitive circuit current leads voltage by 90 degrees. As the circuit is turned on to charge a capacitor, the current through it is maximum, but the voltage and electric field between the plates are zero. Once the capacitor is fully charged, the current is zero but the voltage and electric field are maximum. Electric field is proportional to static charges accumulated on the plates of capacitor.

An inductor stores its energy in form of magnetic field which results from moving charges. In a pure inductive circuit current lags voltage by 90 degrees. As the circuit is turned on to 'charge' an inductor, the current through it and magnetic field around it are zero but the voltage is maximum. Once the inductor is fully 'charged', the current and magnetic field around it are maximum but the voltage is zero. Magnetic field around an inductor is proportional to the current flowing through it.

**Question 1:**

In an AC circuit, current flows one way for a half cycle and flows the other way round the other half cycle. In other words, source polarities get switched every half cycle. A half cycle is taken from 0 degrees to 180 degrees; or from 0 to π to in radian measure.

RMS value of an alternating current is its effective heating value equivalent to a DC current.

In a DC circuit one can simply use the formula Q=CV to find the charges accumulated on capacitor plates. How do we find the charges accumulated on capacitor in an AC circuit? I think that average value of voltage should be used instead of RMS because we are only interested in knowing the average quantity of charge flowing into a capacitor during a half cycle. Average value of sinusoidal voltage waveform is 0.637×Vpk where "Vpk" is peak value of the sinusoidal voltage [1]. The formula could be modified as Q=CV=C*(0.637×Vpk). Do I have it right?

**Question 2:**

In my view, we have missed an important point above to make things simpler. In a half cycle once the capacitor has been charged, the polarities of source get switched. Now the positive of the source is connected to negative of capacitor and so on. First, the capacitor needs to get discharged and it will definitely take some time. Once the discharging has taken place, the charging phase will start. All this is going to happen over a single half cycle. So, my question if the formula, Q=CV=C*(0.637×Vpk), for the accumulation of charge which assumes charging through out the half cycle is still valid because, in my view, during a small part of the given half cycle, no charging is taking place rather discharging is taking place.

References:

[1] https://www.electronics-tutorials.ws/accircuits/average-voltage.html