First-order RL breakpoint terminology: In a first-order RL network used as a filter, the frequency at which XL equals R is called the ________.

Introduction / Context:
First-order RL and RC filters have a single breakpoint that defines where the response transitions from passband to stopband. For an RL filter, this occurs where the reactive impedance equals the resistive component. The terminology for this frequency is widely standardized in filter theory and instrumentation.

Given Data / Assumptions:

• First-order RL network (either low-pass or high-pass depending on output pick-off).
• Sinusoidal steady state, ideal components.
• Definition of inductive reactance XL = 2 * pi * f * L.

Concept / Approach:
The cutoff (also called corner or break) frequency f_c occurs when the magnitude of the reactive impedance equals the resistance: XL = R. Solving gives f_c = R / (2 * pi * L). At this frequency, the magnitude of the transfer function is 1/sqrt(2) of the passband value (−3 dB point) for the standard one-pole filter. “Resonant frequency” does not apply because resonance requires energy exchange between inductance and capacitance, and an RL alone does not resonate.

Step-by-Step Solution:

Verification / Alternative check:
Measurement of an RL low-pass across the resistor shows −3 dB amplitude at f = R / (2 * pi * L), confirming the break-frequency definition.

Why Other Options Are Wrong:
“Optimum frequency” is not a standard filter term. “Bandwidth characteristic” is a graph, not a frequency. “Resonant frequency” requires an LC network.

Common Pitfalls:
Calling any notable frequency “resonant” even when no capacitor is present; mixing up RL with RC formulas (RC has f_c = 1 / (2 * pi * R * C)).

Final Answer:
cutoff frequency