RL impedance with frequency: As the excitation frequency increases, how do the magnitudes of the equivalent impedances of series RL and parallel RL circuits change?

Introduction:
Frequency dependence of impedance is a core idea in AC circuit design and filter selection. Resistor–inductor (RL) networks exhibit different behaviors in series and parallel configurations, but both are governed by the inductor's reactance, which grows with frequency. This question asks you to identify the overall trend for each topology as frequency rises.

Given Data / Assumptions:

• Ideal components: R is frequency independent; L has reactance XL = ω * L.
• Small-signal sinusoidal steady state.
• We are concerned with impedance magnitude trends, not phase.

Concept / Approach:
Series RL: Zs = R + jXL → |Zs| = sqrt(R^2 + (ωL)^2); as ω increases, |Zs| increases monotonically. Parallel RL: The inductor branch impedance XL increases with frequency, so its branch current diminishes; the equivalent impedance approaches R from below as frequency rises, meaning |Zp| increases toward R (and can exceed the low-frequency value set by the parallel of R and a small XL).

Step-by-Step Solution:

Verification / Alternative check:
Plotting |Zs| vs frequency shows a rising curve; plotting |Zp| vs frequency shows a rising asymptote approaching R. SPICE simulations confirm reduced inductor current at high frequency in the parallel branch, raising total impedance.

Why Other Options Are Wrong:

• Both decrease: Contradicts XL = ωL growth.
• Series decreases / parallel increases: Series behavior is opposite; |Zs| increases.
• Series increases / parallel decreases: Parallel impedance does not decrease; it grows toward R as the inductor stops shunting current.

Common Pitfalls:
Confusing high-frequency inductor as a short (that is true at low frequency); forgetting to analyze admittance for the parallel case; overlooking that we ask for magnitudes, not phase.

Final Answer:
both series and parallel RL impedance increase