Which statements about an ideal capacitor's behavior are correct in circuit theory (choose the best overall statement)?

Introduction:
Capacitors are energy-storage elements whose current-voltage relationship is i = C * dv/dt. This relationship yields several widely used rules of thumb about transient and steady-state behavior. The question asks you to identify the consolidated truth among the listed statements.

Given Data / Assumptions:

• Ideal capacitor with capacitance C (no leakage, ESR, or ESL).
• Standard circuit-theory interpretations of "instantaneous" and "dc steady state".
• Small-signal, linear operating region.

Concept / Approach:
Because i = C * dv/dt, an instantaneous voltage step (large dv/dt) implies a very large current impulse; conversely, changing the capacitor's voltage requires time (non-instantaneous) unless infinite current is available. In dc steady state (dv/dt = 0), the current is zero, so the ideal capacitor behaves as an open circuit.

Step-by-Step Solution:
1) Voltage cannot jump instantly: that would require infinite current since dv/dt would be infinite.2) For fast transients, the capacitor presents very low impedance, effectively shunting rapid changes and acting "like a short" for the highest-frequency components.3) At dc steady state, dv/dt = 0, so i = 0 and the capacitor behaves as an open circuit.4) Therefore, each individual statement is correct; the combined best choice is "All of the above".

Verification / Alternative check:
Frequency-domain view: Xc = 1 / (2 * pi * f * C). As f → ∞, Xc → 0 (short-like). As f → 0 (dc), Xc → ∞ (open-like). This confirms the time-domain reasoning.

Why Other Options Are Wrong:
Any single statement alone (a, b, or c) is incomplete; the question asks for the best comprehensive truth.
None of the above: contradicts standard capacitor behavior taught in basic circuit theory.

Common Pitfalls:
Confusing "short to instantaneous changes" with "short to all AC". Real capacitors have finite impedance and parasitics; only very high-frequency components see near-short behavior.

Final Answer:
All of the above