Foundational Physics

Short Answer: A capacitor can still have voltage after being disconnected from a battery because opposite charges remain separated on its plates. These charges create an electric field and a potential difference, even when the battery is no longer connected.

What does the battery do before disconnection?

When a capacitor is connected to a battery in a charging circuit, the battery moves charge through the external wires so that one plate gains excess electrons and the other has a corresponding electron deficit. The plates become oppositely charged.

That charge separation produces an electric field between the plates, along with a voltage across the capacitor.

Why doesn’t the voltage vanish when the battery is removed?

Unplugging the battery removes the source that originally established the charge separation. But if the capacitor’s terminals are left electrically isolated, there is no conducting path for the excess charge to flow from one plate to the other.

The separated charge remains, so the electric field and voltage remain too. The battery is needed to charge the capacitor, not to continuously maintain the voltage of an ideal isolated charged capacitor.

How are charge, capacitance, and voltage related?

For an ideal capacitor, the magnitude of the charge on either plate and the voltage between the plates are related by

Q = CV

Equivalently, V = Q/C. If the capacitor’s charge Q remains constant after disconnection and its capacitance C does not change, its voltage V remains constant.

Can we see this with a simple example?

Suppose a 100 μF capacitor is charged to 12 V. The magnitude of the charge on either plate is

Q = (100 μF)(12 V) = 1.2 mC

In the ideal model, if the capacitor is disconnected with its terminals isolated and its capacitance unchanged, the 1.2 mC of charge separation remains and so does the 12 V potential difference.

That does not mean the capacitor contains unlimited energy or can supply a steady current forever. Connecting a load provides a discharge path, and its voltage can then decrease.

Does a real capacitor hold its voltage forever?

No. Real capacitors have small leakage currents, and moisture, contamination, measurement equipment, or connected components can provide discharge paths. Their voltage generally declines over time, sometimes quite slowly.

This is why a disconnected capacitor may still be charged even though its voltage does not stay constant indefinitely.

The takeaway

Removing the battery does not automatically remove the charge on a capacitor’s plates. As long as separated charge remains, the capacitor can maintain an electric field and voltage without an attached power source.

When This Breaks

The constant-voltage conclusion assumes a capacitor that is isolated, has negligible leakage, and keeps the same capacitance. If charge leaks away or a conducting discharge path is connected, the voltage changes.

Even with charge conserved, changing the plate separation or dielectric can change capacitance and therefore voltage. Real capacitors also have voltage limits and nonideal behavior. Do not treat an open circuit as proof that a capacitor is discharged.

Keep Exploring: Capacitance and Dielectrics

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