Which statements about an ideal capacitor's behavior are correct in circuit theory (choose the best overall statement)?
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AA capacitor acts like a short to instantaneous changes in current.
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BA capacitor's voltage cannot change instantaneously.
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CA capacitor acts like an open to dc.
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DAll of the above
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ENone of the above
Answer
Correct Answer: All of the above
Explanation
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