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Up to: Quick math and science observations

RC- low pass:
(take voltage across resistor)
LOW f: we are giving the capacitor time to lower its voltage, and increase the voltage across the resistor. remember, the voltage across the resistor and capacitor sum to the total voltage. HIGH f: we aren't giving the capacitor time to discharge (and lower its voltage), so the resistor doesn't have much voltage across it.

RC - high pass: (take voltage across capacitor) LOW f: we are giving the capacitor time to discharge, so resistor gets most of the voltage drop

HIGH f: we aren't giving the capacitor time to discharge, so it keeps the voltage drop. resistor gets very little.

RLC filter (parallel)

the L and C connected in parallel have high impedence, so the circuit passes those resonant frequencies.