Why does a capacitor block DC but let AC pass?
A capacitor's opposition is Xc = 1/(ωC).
A capacitor's opposition is Xc = 1/(ωC). For DC the frequency is zero, so Xc is infinite — once charged, the capacitor stops the current, i.e. it blocks DC. For AC, ω is non-zero, so Xc is finite and the plates charge and discharge every cycle, letting AC 'pass through'. Higher frequency → smaller Xc → easier passage.
Key point
Xc = 1/(ωC): infinite at DC (blocks), finite for AC (passes).
Common mistake
thinking charge physically crosses the gap between the plates.
Memory tip
capacitor: blocks DC, passes AC (and passes high frequencies best).
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