DC Blocking Capacitor

It is often said that capacitors block DC or equivalently, that a capacitor is an open circuit at DC. But is this true? Actually, no, it is not true. What is true is that the DC steady state current through a capacitor is identically zero. In DC steady state, all circuit voltages and currents are constant. By the fundamental capacitor equation:


i=C*(dV/dt)

we can see that this is the case.

Examining the equation answers your question, however. In steady state DC all currents and voltages are constant, so the deriovative of a constant voltage potential = 0, simple enough. On the other hand, when an AC voltage is applied, voltage is alternating at some frequency so this derivative is not zero (it's only zero at the peaks of the positive and negative cycle, at values of +- signal amplitude (it's just a sine wave signal) - everywhere else the derivative is non-zero so a current flows across the capactor by definition.

Simply talking if neglecting the internal resistance of capacitor
i=V/Xc = V*2πf *C
where Xc is the capacitive reluctance = 1/(W*C)=1/(2πf *C)
where f is the frequency of current which = 0 in case of DC current
so i=0 and blocked.

while f has a value in hertz in case of AC current so i is not zero.