Question

A DC current does not go through the capacitor after the initial charging. Check the equation that describes the impedance in RC circuits when the frequency f decreases to zero (which is the case of any DC current). Explain qualitatively why an AC current can go through a capacitor , but a DC current cannot.

Answer 1

1. Mahtematically: The Impedance (Reactance with no Resistance) of the capacitor Xc = 1 / (2*Pi*f*C).For D.C. frequency f = 0. Then Xc = infinity and D.C. Current is blocked and does not flow.For A.C. f is not Zero and hence A.C. Current can flow.

2. D.C.Transients Point of view.:The Property of Capacitance is that the Capacitance acts initially as a Short Circuit and finally as an Open Circuit,for D.C. Excitation. The Voltage across a Capacitor does not change all on a sudden.While charging it charges from zero to full voltage and while discharging it discharges from full voltage to zero,both exponentially.This is the Principle used in Wave Shaping in Pulse and Digital Circuits.

3. From Charging Point of View: In the case of D.C. the Capacitor charges fully to the Charging Voltage and the Voltage across it will be equal to the Charging Voltage in nearly 5 times the Time Constant. In the case of D.C. the Voltage across the capacitance does not change after full charging and remains equal and opposite to the D.C. Voltage across it and hence no current can flow through it.
In the case of A.C., after full charging the Voltage across the capacitance decreases and reverses and so does the A.C. current through the capacitor.

4. From Field Theory Point of view: The Current through the capacitance is only a Diffusion Current. Diffusion Current Density, Jd = Partial differential of Vector D with reference to time, and the Electric Flux Density D remains constant in the case of D.C. after the Capacitor is charged fully.

5. From Circuit Theory Point of View: The Current through the Capacitance i = C* ( dv / dt ). In the case of D.C. V is constant and if C is Constant then i = 0. Generally C is constant as it depends on the Geometry and the Dielectric Constant of the Capacitor Medium.