Series R, L, and C

Let's take the following example circuit and analyze it: (Figure below)

Example series R, L, and C circuit.

The first step is to determine the reactances (in ohms) for the inductor and the capacitor.

The next step is to express all resistances and reactances in a mathematically common form: impedance. (Figure below) Remember that an inductive reactance translates into a positive imaginary impedance (or an impedance at +90^o), while a capacitive reactance translates into a negative imaginary impedance (impedance at -90^o). Resistance, of course, is still regarded as a purely “real” impedance (polar angle of 0^o):

Example series R, L, and C circuit with component values replaced by impedances.