Question

What is the unit of capacitive reactance \[{X_c}\] ?

Answer 1

Hint: The reactance of any network is the measure of opposition of current through the circuit. Capacitive reactance is the measure of opposition of current by a capacitor.We know that capacitor is charged plate kept parallel. When it is connected in an AC circuit it lets the AC current flow but blocks the DC. But the AC current does not flow without any opposition due to reactance. The current is opposed in the circuit and lags the voltage with time.The measure of this opposition is similar to that of resistance.

Complete answer:
The capacitive reactance also varies with the capacitance of the circuit just like resistance. The mathematical expression for capacitive reactance is given by,
\[{X_c} = \dfrac{1}{{j\omega C}}\] or \[\left| {{X_c}} \right| = \dfrac{1}{{\omega C}}\]
where, \[{X_c}\] is the capacitive reactance, \[\omega \] is the angular frequency of the source voltage, \[C\] is the capacitance of the circuit and is the iota (\[j = \sqrt { - 1} \]).\[\left| {{X_c}} \right|\] is the magnitude of the capacitive reactance.

So, we can clearly see that the reactance varies with the frequency and the capacitance of the capacitor. Since, the measure of reactance is just the measure of opposition in the circuit just like resistance, so the unit is also the same for both of them.

Hence, the unit of capacitive reactance is ohm (\[\Omega \]).

Note: The expression of reactance of any circuit is given by, \[R + jX\] where, \[X\] is the capacitive or inductive reactance of the circuit and \[R\] is the resistance. The heat loss through an inductive or capacitive circuit is zero since the energy gets stored in the field or in form of charge. This is why capacitive or inductive circuit is called purely reactive circuit