Capacitance Basics, Impedance And Capacitive Reactance

The Voltage And Current Relationship OF Capacitors

Connect the capacitor to both ends of the AC power supply, attach a voltmeter and ammeter to view the waveform:

Under the excitation of alternating current, the relationship between voltage and current on the capacitor is as follows:

It can be seen that both the voltage and current waveforms are sine waves, and the current waveforms are 90° (π/2) ahead of the voltage waveforms in phase, or 270° (3π/2) behind. But we're still used to talking about 90° (π/2) ahead.

Among them, we explain the charge and discharge process of the capacitor under the excitation of the DC power supply in detail: the DC power supply charges the capacitor, at the beginning of charging, the capacitor current is the largest, 

the voltage is 0, and the circuit is equivalent to short circuit; After charging, the current is 0, the capacitor voltage is maximum, and the circuit is equivalent to an open circuit. A similar process occurs in AC, 

where the peak of the current corresponds to a voltage of 0V and the peak of the voltage corresponds to a current of 0A, so the phase difference is 90° (π/2).

Resistance OF Capacitors - Capacitive Reactance

The formula for calculating the tolerance is as follows:

It can be seen that the size of the capacitive reactance is related to the capacitance capacity and signal frequency. Below, we increase the capacity of the capacitor in the previous example from 1000uF (1mF) to a large 10000uF (10mF), and take a look at the effect:

In the figure, the phase difference between current and voltage does not change, but due to the increase of capacitance capacity, the capacitance reactance becomes smaller, so the current becomes larger than 50A (previously it was 5A).

For the impedance calculation of a mixture of capacitance, inductance and resistance, it is more complicated, and we will skip it here:

For the impedance calculation of pure capacitor or pure inductive circuit, in the phase problem, some students can not remember whether the capacitor current is ahead of the voltage, 

or the inductor current is ahead of the voltage, always confused. Here is a trick, is to imagine an English word - "ICE" (ICE), I stands for current, C stands for capacitance, E stands for voltage,

 in the word "ice" I ahead of E, representing the phase characteristics of the current and voltage on the capacitor, is this easier to remember?

Reactance formula: Xc = 1/ωc

(100+ J200-J400)/(100+j200)*(-j400)=-32+24j. This is the calculation of complex numbers, which can be calculated by repeated deformation.

Experiments show that the capacitive reactance is inversely proportional to the capacitance, and also inversely proportional to the frequency.

 If the capacitive reactance is expressed by Xc, the capacitance is expressed by C, and the frequency is expressed by f, then the capacitive reactance under sinusoidal alternating current is obtained

Xc = 1 / (2 PI fC)

Xc = 1/ (ωC) = 1/ (2πfC)

Xc-------- capacitance reactance value; ohm

ω--------- angular frequency (angular velocity)

PI --------- PI, which is about 3.14

f--------- frequency

C--------- Capacitance in farad