Seriesresonanssissa

Seriesresonanssissa, often translated as series resonance, is a phenomenon that occurs in an electrical circuit containing an inductor and a capacitor when the frequency of the applied alternating voltage causes the inductive reactance to equal the capacitive reactance. At this specific frequency, known as the resonant frequency, the impedance of the circuit reaches its minimum value.

The resonant frequency, denoted by $f_r$, can be calculated using the formula $f_r = 1/(2\pi\sqrt{LC})$, where L is the inductance in henries and C is the capacitance in farads. When a circuit is in series resonance, the total impedance ($Z$) is purely resistive. This is because the inductive reactance ($X_L = 2\pi fL$) and the capacitive reactance ($X_C = 1/(2\pi fC)$) have equal magnitudes but opposite phases, effectively canceling each other out. The impedance in a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$. At resonance, $X_L = X_C$, so $Z = \sqrt{R^2 + 0^2} = R$.

This condition leads to a significant increase in the current flowing through the circuit, as the impedance is at its lowest. If the resistance R is very small, the current can become extremely large. This characteristic makes series resonant circuits useful in applications where selectivity is desired, such as tuning circuits in radio receivers, where they can amplify signals at the resonant frequency while attenuating others. Conversely, the large current at resonance can be a concern in power systems, potentially leading to excessive stress on components if not properly managed.