Q.Why does a capacitor block DC whereas an inductor allows easy path to it?

A capacitor blocks DC (acts as a perfect insulator) but allows AC to pass.

The reactance of a capacitor is:

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi f C}$

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$X_L=\omega L$, and DC has $\omega=0$, so $X_L=0$ for DC — both statements true, and R explains A.

For DC, the frequency is zero, so the angular frequency $\omega=2\pi\nu=0$. The inductive reactance is $X_L=\omega L$, so for DC, $X_L = 0\times L = 0$. This means an ideal inductor offers zero impedance (zero opposition) to a steady direct current — Assertion A is true. Reason R correctly states both the fact that DC has (essentially) zero frequency and the f …

Inductive reactance X_L = ωL; for steady DC, ω = 0, so X_L = 0.

The inductive reactance is $X_L = \omega L = 2\pi f L$.

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