How does the capacitor behave in the AC circuit?

If the AC power source is connected to a resistor, the current and voltage in the circuit at any point in the time diagram will be proportional to each other. This means that the current and voltage curves will reach a "peak" value at the same time. At the same time we say that the current and voltage are in phase.

Let us now consider how the capacitor behaves in an AC circuit.

If a capacitor is connected to the AC voltage source, the maximum voltage value on it will be proportional to the maximum value of the current flowing in the circuit. However, the wave peak of the voltage sinusoid will not attack at the same time as the maximum current.

In this example, the instantaneous current reaches its maximum value by a quarter period (90 e. G.) Earlier than the voltage does. In this case, they say that "the current is ahead of the voltage by 90◦."

Unlike the situation in the dc current circuit, the V / I value here is not constant. Nevertheless, the ratio V max / I max is a very useful value and in electrical engineering is called the capacitive resistance (Xc) of the component. Since this value still reflects the ratio of voltage to current, i.e. In the physical sense is resistance, its unit of measurement is Om. The value Xc of the capacitor depends on its capacitance (C) and the frequency of the alternating current (f).

Since an RMS voltage value is applied to the capacitor in the AC circuit, the same alternating current flows in this circuit, which is limited by the capacitor. This limitation is due to the reactance of the capacitor.

Therefore, the value of the current in the circuit, which does not contain any other components other than the capacitor, is determined by an alternative version of Ohm's Law

I _RMS = U _RMS / X _C

Where U _RMS is the root-mean-square (effective) value of the voltage. Note that X _c replaces the R value in the Ohm law version for DC.

Now we see that the capacitor in the AC circuit behaves quite differently than the constant resistor, and the situation here, accordingly, is more complicated. In order to better understand the processes taking place in such a chain, it is useful to introduce such a concept as a vector.

The basic idea of a vector is the notion that the complex value of a time-varying signal can be represented as a product of a complex number (which does not depend on time) and some complex signal that is a function of time.

For example, we can represent the function A cos (2πνt + θ) simply as a complex constant A ∙ e ^jΘ .

Since vectors are represented by magnitude (or module) and angle, they are represented graphically by an arrow (or vector) rotating in the XY plane.

Taking into account the fact that the voltage on the capacitor "lags" in relation to the current, the vectors representing their vectors are located in the complex plane as shown in the figure above. In this figure, the current and voltage vectors rotate in a direction opposite to the clockwise direction.

In our example, the current on the capacitor is due to its periodic recharging. Since the capacitor in the AC circuit has the ability to periodically accumulate and discharge an electric charge, there is a constant exchange of energy between it and the power source, which in electrical engineering is called reactive.