⦿ Chapter : Alternating current (AC) ⦿ Topic : Alternating current circuit containing capacitor only and phasor diagram ...
Capacitance in AC Circuits results in a time-dependent current which is shifted in phase by 90o with respect to the supply voltage producing an effect known as capacitive reactance.
When capacitors are connected across a direct current DC supply voltage, their plates charge-up until the voltage value across the capacitor is equal to that of the externally applied voltage. The capacitor will hold this charge indefinitely, acting like a temporary storage device as long as the applied voltage is maintained.
During this charging process, an electric current ( i ) flows into the capacitor which results in its plates beginning to hold an electrostatic charge. This charging process is not instantaneous or linear as the strength of the charging current is at its maximum when the capacitors plates are uncharged, decreasing exponentially over time until the capacitor is fully-charged.
This is because the electrostaic field between the plates opposes any changes to the potential difference across the plates at a rate that is equal to the rate of change of the electrical charge on the plates. The property of a capacitor to store a charge on its plates is called its capacitance, (C).
Thus a capacitors charging current can be defined as: i = CdV/dt. Once the capacitor is “fully-charged” the capacitor blocks the flow of any more electrons onto its plates as they have become saturated. However, if we apply an alternating current or AC supply, the capacitor will alternately charge and discharge at a rate determined by the frequency of the supply. Then the Capacitance in AC circuits varies with frequency as the capacitor is being constantly charged and discharged.
We know that the flow of electrons onto the plates of a capacitor is directly proportional to the rate of change of the voltage across those plates. Then, we can see that for capacitance in AC circuits they like to pass current when the voltage across its plates is constantly changing with respect to time such as in AC signals.
However, they do not like to pass current when the applied voltage is of a constant steady state value such as in DC signals. Consider the circuit below.
In the purely capacitive circuit above, the capacitor is connected directly across the AC supply voltage. As the supply voltage increases and decreases, the capacitor charges and discharges with respect to this change. We know that the charging current is directly proportional to the rate of change of the voltage across the plates with this rate of change at its greatest as the supply voltage crosses over from its positive half cycle to its negative half cycle or vice versa at points, 0o and 180o along the sine wave.
Consequently, the least voltage rate-of-change occurs when the AC sine wave crosses over at its maximum positive peak ( +VMAX ) and its minimum negative peak, ( -VMAX ). At these two positions within the cycle, the sinusoidal voltage is constant, therefore its rate-of-change is zero, so dv/dt is zero, resulting in zero current change within the capacitor. Thus when dv/dt = 0, the capacitor acts as an open circuit, so i = 0 and this is shown below.