Capacitors connect voltage change to current

Voltage cannot jump without an impulse

An ideal capacitor stores charge according to $q=CV$ and has current $i=C\,dV/dt$ under the passive sign convention. It resists an instantaneous voltage change because that would require an impulse of current. It does not resist voltage itself: a charged capacitor can remain at a nonzero voltage while carrying zero DC current.

At a settled DC operating point, an ideal capacitor is open circuit. During a transition, it is a dynamic element and cannot simply be removed. Its initial voltage matters. A real capacitor also has leakage, equivalent series resistance, dielectric effects, and a voltage rating. The ideal model intentionally omits those properties until they are relevant to the calculation.

Worked ramp and energy

Drive a 1 μF capacitor with a constant 1 mA current. Then $dV/dt=0.001/0.000001=1000$ V/s, or 1 V/ms. Starting at 0 V, the capacitor reaches 2 V after 2 ms, provided the current source can maintain that current at the required voltage. Charge is 2 μC. Stored energy is $E=CV^2/2=2$ μJ.

This energy result is different from charge: charge scales linearly with voltage, while energy scales with voltage squared. Doubling the voltage to 4 V doubles charge but quadruples stored energy to 8 μJ. Units make the distinction clear: coulombs are not joules.

Initial conditions are part of the problem

A 1 μF capacitor already at 1 V reaches 2 V after only 1 ms under the same 1 mA current. Connecting two charged capacitors abruptly is not explained by calling both “open at DC”; the transition and wiring resistance must be modeled. Likewise, shorting a charged capacitor may produce a current pulse beyond the source's ordinary steady current.

For course calculations, state capacitance, initial voltage, imposed current or surrounding resistance, and time interval. Before a real low-voltage measurement, verify polarity for polarized parts and discharge stored charge through an appropriate resistor. For changing signals, ask about current and time before applying a steady-state shortcut.