What is the approximate magnitude of the impedance of a series R-L-C circuit at resonance?

At resonance in a series R-L-C circuit, the impedance reaches its minimum value, which is approximately equal to the circuit resistance (R). This occurs because, at the resonant frequency, the inductive reactance (XL) and capacitive reactance (XC) cancel each other out, resulting in a situation where the only impedance left affecting the circuit is that of the resistor.

In more technical terms, the resonant condition is achieved when the frequency of the input signal matches the natural frequency of the circuit, causing the reactances to equal each other (XL = XC). Consequently, the formula for impedance at resonance simplifies to Z = R, where Z is the total impedance and R is the resistance.

This characteristic of resonance highlights its importance in tuning circuits for radios and other communication devices, where selecting specific frequencies is crucial to performance. The other options suggest conditions that do not accurately represent the behavior of a series R-L-C circuit at resonance; they don't account for the fundamental relationship between resistance and reactance in this state.