Question

If you use a parallel plate capacitor with air in the gap between the plates as part of a series RLC circuit in a generator, you can measure current flowing through the generator. Why is it that the air gap in the capacitor does not act like an open switch, blocking all current flow in the circuit?

Short answer

Answer: The air gap in a parallel plate capacitor in a series RLC circuit does not act like an open switch because the capacitor stores and releases energy as an electric field, which allows an alternating current (AC) to flow through the circuit. As the frequency of the applied signal increases, the capacitive reactance decreases, allowing more current to flow through the capacitor.

Step-by-step solution

Capacitor functionality

A capacitor is an electronic component that can store and release electrical energy. In a parallel plate capacitor, two conductive plates separated by a dielectric (air, in this case) are used. When a voltage is applied across the capacitor, an electric field is established, and as a result, positive and negative charges accumulate on the plates. The energy is stored in this electric field until the voltage is removed or changed.

Series RLC circuit

A series RLC circuit is a combination of a resistor (R), an inductor (L), and a capacitor (C) connected in series. In this circuit, the voltage across all the components (V_R, V_L, and V_C) is equal to the total voltage of the circuit (V_T). The current (I) passing through each component is the same due to the series connection, while the voltages of each component differ. The voltage across the resistor is in phase with the current, while for the inductor and capacitor, there's a 90-degree phase difference.

Role of air gap

In a capacitor with an air gap, the air acts as a dielectric material between the two plates. This dielectric prevents the flow of charge directly between the plates. Nevertheless, a current does flow into and out of the plates as energy is stored and released by the capacitor.

Alternate current (AC) and capacitive reactance

In an AC circuit, the current alternates directions, and the voltage across the capacitor's plates also changes periodically. As the stored energy depends on the voltage applied, this energy storage and release process happens cyclically resulting in AC current flowing through the circuit. The effective opposition to the flow of AC current in a capacitor is known as capacitive reactance (X_C), which is calculated as X_C = 1/(2πfC), where f is the frequency of the AC signal and C is the capacitance. It shows that the current flowing through the air gap capacitor is inversely proportional to its reactance, meaning that as the frequency of the AC signal increases, the reactance decreases, and more current flows through the capacitor.

Conclusion

The air gap in a parallel plate capacitor in a series RLC circuit does not act like an open switch because the capacitor stores and releases energy as an electric field, which allows an alternating current (AC) to flow through the circuit. As the frequency of the applied signal increases, the capacitive reactance decreases, allowing more current to flow through the capacitor.