Question

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?

Answer 1

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

Step-by-step 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.