Question

Explain why the reactance provided by a capacitor to an alternating current decreases with increase in frequency?

Answer 1

In this problem we need to understand the working of a capacitor, when it passes current only at the time of charging and discharging. And after that we need to understand the flow of AC current through a capacitor (what actually affects the flow of AC current). The above two points together will be enough to solve the problem.

Formula used:
${R_C} = \dfrac{1}{{\omega C}}$
Where, ${R_C}$ is the reactance offered, $\omega$ is the frequency of the AC current and $C$ is the capacitance of the capacitor.

Complete step by step answer:
Reactance (electrical reactance) is defined as the opposition offered to the flow of current from a circuit element due to the inductance and capacitance of the circuit element. Greater reactance leads to smaller currents for the same applied voltage.Now the reactance formula for a capacitor is:
${R_C} = \dfrac{1}{{\omega C}}$

Now from the above equation it is clear that with the increase in frequency of the alternating current the net reactance of the capacitor decreases thus the amount of current passing through the capacitor increases.If we see a general scenario a capacitor passes current only when it is charging or discharging (thus, in DC current the flow of current stops after a while as the capacitor becomes fully charged).

In AC current the voltage around the capacitor keeps on changing thus the capacitor allows the flow of current through itself due to this voltage change (as it keeps on charging and discharging). So, when the rate of change of voltage across the capacitor increases the current flowing also increases (as rate of current flow is directly proportional to the rate of charging and discharging).

Note: In case if the question had asked the same about inductors instead of capacitors the answer becomes completely different. The reactance of an inductor increases with the increase in the frequency of the alternating current as $\left( {{R_L} = \omega L} \right)$ (where ${R_L}$ is the reactance of the inductor, $\omega$ is the frequency of the AC current and $L$ is the inductance of the inductor) for inductor, so we can see from the formula that the reactance of the inductor is directly proportional to the frequency of the alternating current.