Capacitors in basic circuits — identify the correct statement In ideal circuit theory, select the single true statement about how a capacitor behaves under DC and during transients.

Introduction / Context:
Understanding transient behavior of capacitors is foundational for electronics. Learners often hear rules of thumb like “capacitors block DC and pass AC,” but the precise, time-domain statement that governs all ideal capacitor behavior is that its voltage cannot jump instantaneously.

Given Data / Assumptions:

• Ideal components (no series resistance, no leakage).
• DC and transient (step) excitations considered.
• Focus on qualitative correctness of statements.

Concept / Approach:
An ideal capacitor obeys i = C * dv/dt. This equation ties current to the time rate of change of voltage. Because dv/dt would need to be infinite for a finite-time jump in voltage, and that would require infinite current, an instantaneous change in capacitor voltage is impossible in any physical circuit. Conversely, current can change immediately when the applied voltage slope changes.

Step-by-Step Solution:
Start from i = C * dv/dt.Assume a finite current: then dv/dt is finite, so v cannot jump.For a DC steady state after long time, dv/dt = 0, so i = 0 and the capacitor behaves as an open circuit to DC.Immediately after a voltage step, the capacitor initially looks like a short for the transient current path because its initial voltage is fixed, not because it is a permanent short.

Verification / Alternative check:
Consider a step voltage V applied through a resistor R to a capacitor C. The capacitor voltage follows vC(t) = V * (1 - e^(-t/(R*C))). There is no discontinuity at t = 0; instead, a smooth exponential rise proves there is no instantaneous voltage change.

Why Other Options Are Wrong:

• A fully charged capacitor as a short to DC: wrong; it is an open circuit at steady DC.
• Current in a capacitive branch cannot change instantly: wrong; current may change abruptly when dv/dt changes.
• An uncharged capacitor always open for a step: wrong; right after a step, it initially conducts (appearing like a short for an instant) while its voltage starts from its initial value.

Common Pitfalls:

• Confusing initial transient behavior with steady-state DC behavior.
• Assuming “short to DC” because large surge current flows briefly; in steady state, that current decays to zero.

Final Answer:
The voltage across an ideal capacitor cannot change instantaneously.