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There is something I'm struggling to understand about passive RC filters: When considering a simple low pass RC loop, what exactly is the gain/output at DC and low frequencies? I've been assuming two possible events:

  1. The input charges the capacitor, setting the output equal to input as soon as the capacitor is charged;

  2. Due the high reactance of the capacitor at DC and low frequencies, the current, the capacitor can be ignored, and thus there is a small drop across the resistor, which will depend on the load resistance and current.

However, both seem to contradict each other, particularly as to whether or not there is an actual voltage drop across the resistor.

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up vote 4 down vote accepted

Both correctly describe how an RC filter will react at DC. The reason you see a contradiction is because you're actually describing two different situations: loaded, and unloaded. If there's a load, there's current flow from the source, through the resistor, to the load. The voltage drop across the resistor will be \$V=IR\$. If there's not a load, there's no current flow, so there's no voltage drop across the resistor.

Now, when you say "at low frequencies", as long as there's any frequency content, the capacitor will have some effect on the output. But for DC, you seem to understand the analysis correctly.

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