Question

Define the formula for the resonant frequency in a series L-C-R alternating current circuit.

Hint:

At resonance in a series L-C-R circuit, the inductive and capacitive reactances cancel each other, resulting in a minimum impedance equal to the resistance.

Answer 1

In a series L-C-R circuit, resonance occurs when the inductive reactance (\( X_L \)) and capacitive reactance (\( X_C \)) are equal in magnitude but opposite in phase. The formula for the resonant frequency \( f_0 \) of a series L-C-R circuit is given by:
\[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \] where:
- \( L \) is the inductance in henries (H),
- \( C \) is the capacitance in farads (F).
At this frequency, the impedance of the circuit is purely resistive, and the current reaches its maximum value.