This all-in-one online Capacitive Reactance Calculator performs calculations using the formula that relates the frequency of alternating current and the capacitance of an electrical circuit to its reactance. You can enter the values of any two known parameters in the input fields of this calculator and find the missing parameter.
Capacitive Reactance Formula
It is well known that a capacitor consists of two conductors separated by an insulator, and thus is incapable of conducting direct current. But capacitors can conduct alternating current, while providing some resistance to it due to their reactance.
The fact is that a capacitor included in a circuit through which an alternating current flows does not all the time prevent the movement of charges in this circuit.
At the moment the electric voltage is connected in the circuit, electric charges begin to move and accumulate on the capacitor plates. The capacitor prevents the flow of current only after the time period required to charge the capacitor.
If the direction of the current flow is reversed, then the capacitor begins to discharge and recharge. And all this time, current flows through the capacitor. Therefore, the capacitor does not actually conduct current only during the period of time when it is fully charged and the direction of the current has not yet changed.
Thus, it is clear that the time-averaged ‘resistance’ of a capacitor depends both on its capacitance and on the frequency of the alternating current. The ‘resistance’ to the current that can be passed by a capacitor is called the capacitive reactance.
Although the reactance of a capacitor is different from the resistance of a resistor, but it is measured in Ohms just the same. Capacitive reactance is used instead of ordinary resistance in calculations using Ohm’s law.
The capacitive reactance of a circuit is expressed by the following formula, which is used in our Capacitive Reactance Calculator:
$$X_c = \frac{1}{2\pi fC},$$
where
\(X_c\) is the capacitive reactance measured in the SI system in ohm (Ω). Dimension: M·L2·T-3·I-2,
\(C\) is the capacitance measured in the SI system in farad (F). Dimension: M-1·L-2·T4·I2,
\(f\) is the frequency measured in the SI system in hertz (Hz) : 1 Hz = 1 sec -1 .
From this formula we can see that the higher the frequency and the larger the capacitance of the capacitor, the lower the capacitive reactance, which is intuitively understandable from the above description of the process.
It is important to emphasize that capacitive reactance differs from conventional resistance. The current and voltage for a capacitor are 90° out of phase, whereas for a resistor they are in phase. As a result, the resistance of the resistor \(R\) and the reactance of the capacitor \(X_c\) cannot be added up directly. Instead, they should be summed up ‘vectorially’:
$$X_{total} = \sqrt{X_c^2+R^2}.$$
In addition, capacitive reactance does not dissipate electrical energy in the form of heat. Instead, energy is stored in the capacitor for a while and returned to the circuit after a quarter of a cycle, while the usual resistance constantly loses energy.
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