Question
A capacitor blocks DC but allows AC. Explain.

Answer

Capacitive reactance, $X _C=\frac{1}{\omega C}=\frac{1}{2 \pi f c}$
where, $f=0, X_C=\infty$
where $f$ is the frequency of the ac supply. In a dc circuit $f=0$. Hence the capacitive reactance has infinite value for $dc$ and a finite value for ac. In other words, a capacitor serves as a block for dc and offers an easy path to ac.

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