Why use a resistor in filter circuits
Since capacitors and inductors can filter on their own.


Consider the following "filter" consisting of a capacitor on its own:







simulate this circuit &ndash; Schematic created using CircuitLab

Note that, by inspection, \$V_{out} = V_{in}\$ regardless of the presence of the capacitor; there is no filtering taking place.

This is because the output port is identical to the input port.

Now, add a resistor:







simulate this circuit

Note that we now have distinct input and output ports and now we have a 1st order filter.  We could have added in inductor instead of a resistor and created a 2nd order filter. 

$$V_{out}= V_{in}\frac{1}{1+j\omega C_1 R_1}$$