Complete Electronics Self-Teaching Guide with Projects

Resonance

19 Calculations in previous problems demonstrate that capacitive reactance decreases as frequency increases, and that inductive reactance increases as frequency increases. If a capacitor and an inductor are connected in series, there is one frequency at which their reactance values are equal.

Questions

A. What is this frequency called? _____

B. What is the formula for calculating this frequency? You can find it by setting X_L = X_C and solving for frequency. _____

Answers

A. The resonant frequency

B. 2πfL = 1/(2πfC). Rearranging the terms in this equation to solve for f yields the following formula for the resonant frequency (f_r):

20 If a capacitor and an inductor are connected in parallel, there is also a resonant frequency. Analysis of a parallel resonant circuit is not as simple as it is for a series resonant circuit. The reason for this is that inductors always have some internal resistance, which complicates some of the equations. However, under certain conditions, the analysis is similar. For example, if the reactance of the inductor in ohms is more than 10 times greater than its own internal resistance (r), the formula for the resonant frequency is the same as if the inductor and capacitor were connected in series. This is an approximation that you use often.

Questions

For the following inductors, determine if the reactance is more or less than ...