Physics AC Through a Capacitor

Study Notes

Physics AC Through a Capacitor

A capacitor, as mentioned earlier, is a passive electronic device with two terminals. It has the capacity to store electrical energy in an electrical field. When a capacitor is connected to an AC voltage source, the current will flow for the duration required to charge the capacitor. Let's delve deeper into what happens within the capacitor during an AC cycle.

AC Voltage Source Applied Across a Capacitor

Consider an electric circuit with a capacitor and an AC voltage V, represented by the symbol ~, that produces a potential difference across its terminals which vary sinusoidally. The AC voltage can be given by the expression:

vm = amplitude of the oscillating potential difference ω = angular frequency

Due to this varying potential difference, a current will flow through the circuit, but the capacitor itself will only allow passage of current at specific points during the AC cycle. This is because the capacitor behaves as a reactive component, storing energy in its electric field.

Relationship Between Frequency and Capacitance

The capacitive reactance (Xc) of a capacitor depends on both the frequency (ω) and the capacitance (C). The capacitive reactance acts similar to resistance, blocking the flow of current in proportion to its own reactance. Xc is inversely proportional to both frequency and capacitance.

For capacitors in AC circuits, the current lags behind the voltage by 90° with respect to the supply voltage. Additionally, the capacitive reactance is dependent on the frequency and capacitance of the capacitor, meaning the opposition to current flow through the capacitor decreases as the frequency increases. At very high frequencies, the capacitor effectively has zero reactance (acts as a short circuit), while at very low frequencies or DC conditions, the capacitor has infinite reactance (acts as an open circuit).

Charging and Discharging in AC Circuit

When a capacitor is connected to an AC supply, it charges and discharges based on the frequency of the supply. Unlike in a DC circuit, where the capacitor charges until it equals the external voltage, in an AC circuit, the capacitor charges and discharges as the voltage across it changes, leading to a time-dependent current.

Description

Explore the behavior of a capacitor in an alternating current (AC) circuit, understanding how it charges and discharges in response to the varying potential difference across its terminals. Learn about the relationship between frequency, capacitance, and capacitive reactance, and how these factors influence the flow of current through the capacitor.