Series vs. parallel RLC far from resonance: at frequencies well above and well below the resonant frequency, the series RLC network behaves like ______ while the parallel RLC network behaves like ______.

Introduction / Context:
Understanding the limiting behavior of RLC circuits far from resonance allows quick mental checks when sketching Bode plots or predicting filter action. This question contrasts the series and parallel forms when the operating frequency is much lower or much higher than the resonant frequency f0.

Given Data / Assumptions:

• Linear, ideal R, L, and C elements.
• Frequency well below and well above resonance (|ω − ω0| large).
• Qualitative “looks like” refers to net impedance magnitude relative to load: open (very large impedance) vs short (very low impedance).

Concept / Approach:
For a series RLC, the net impedance is Z = R + j(ωL − 1/(ωC)). Far below resonance (ω → 0), 1/(ωC) is very large in magnitude, so |Z| is large; far above resonance (ω → ∞), ωL is very large; either way the series path is “large impedance,” akin to an open. For a parallel RLC, the net admittance is the sum of branch admittances; away from resonance either the capacitor (at high ω) or the inductor (at low ω) provides a very low-impedance path, so the network tends toward a “short.”

Step-by-Step Solution:

Verification / Alternative check:
Impedance loci or Bode plots corroborate: series resonance gives a deep impedance minimum at ω0 and rises sharply away; parallel resonance gives a large impedance maximum at ω0 and falls off away, approaching a short at extremes.

Why Other Options Are Wrong:

• Like a short, like an open: reverses the true limiting behavior.
• Inductive, capacitive / Capacitive, inductive: describe phase, not the open/short magnitude analogy across both extremes.
• Resistive, reactive: too vague and incorrect for the limits described.

Common Pitfalls:
Mixing series vs parallel intuition; focusing on phase sign rather than overall magnitude; forgetting that “open/short” here is a qualitative magnitude analogy, not an exact boundary condition.

Final Answer:
Like an open, like a short