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Taking the Laplace transform of both sides of Eq.(E.1) gives
where we made use of the fact that the impedance of a capacitor is
, as derived above, and the impedance of a resistor
is
just
(since impedance is defined as voltage over current for
electrical systems, or force over velocity for mechanical systems).
The driving point impedance of the whole RC filter is thus
Alternatively, we could simply note that impedances always sum in
series and write down this result directly.
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