Before designing the filter, one must understand the relationship between the output voltage of the circuit and the frequency. For a series RLC circuit, how do the impedances of the circuit elements depend on the frequency?

The impedance for the capacitor is inversely proportional to the frequency, while the impedance for the inductor is directly proportional to the frequency.

Explanation:

A RLC series circuit is formed by a resistor, an inductor and a capacitor in series, the impedance is the oposition to the current caused by the inductor and the capacitor. The impedance for the inductor is given by ZL = i*\omega*L, so the impedance is directly proportional to the frequency (\omega in rad/s). The impedance for the capacitor is given by ZC = -i/(\omega*C), so the capacitor impedance is inversely proportional to the frequency. To convert the frequency from Hz to rad/s we multiply f by 2\pi.