When a capacitor is charged by a battery and the battery is subsequently disconnected, a specific physical state is achieved where the charge stored on the capacitor becomes isolated.
Upon disconnection from the charging battery, the capacitor retains the charge that was transferred to its plates. This is a crucial property for capacitors used in applications where they act as temporary power sources or charge storage devices.
The Effect of Disconnecting the Battery
The primary consequence of disconnecting a charged capacitor from the battery is related to the conservation of charge.
As stated in the provided reference: "The charge on the plates does not change as the capacitor is disconnected from the battery."
This means that once the capacitor is isolated from the external circuit (the battery), the net amount of charge on the positive and negative plates remains constant, assuming no leakage paths exist.
Other properties, such as potential difference (voltage) and stored energy, are then determined by this fixed charge and the capacitor's capacitance. For instance, the reference also notes that after disconnection, "The presence of dielectric slab increases the capacitance, which decreases the potential difference. Thus, the energy stored is reduced." This illustrates that even when disconnected and the charge is fixed, other parameters can change if the physical properties of the capacitor (like the dielectric) are altered.
Why Disconnect a Charged Capacitor?
Disconnecting a charged capacitor from its charging source is common in various electronic circuits and applications:
- Energy Storage: The capacitor holds the stored electrical energy, which can then be discharged into another part of the circuit when needed.
- Filtering: In power supply circuits, capacitors are charged by rectified AC voltage and then disconnected (in effect, during parts of the AC cycle) to smooth out voltage variations, providing a more stable DC output.
- Timing Circuits: The rate at which a capacitor discharges through a resistor after being disconnected from a charging source is used to create time delays.
- Camera Flashes: A capacitor is charged by a battery and then rapidly discharged through a xenon lamp to produce a brief, intense flash of light.
In all these scenarios, the disconnection allows the capacitor to function based on the charge it has accumulated.
Key States: Connected vs. Disconnected
Understanding the difference between a capacitor connected to a battery and one that has been disconnected after charging is fundamental:
| Property | Connected to Battery (Fully Charged) | Disconnected After Charging |
|---|---|---|
| Voltage | Equal to battery voltage | Varies based on charge and capacitance |
| Charge | Determined by battery voltage and capacitance (Q = CV) | Remains constant (as stated in the reference) |
| Current | Approaches zero as it charges | Zero (ideally, no leakage) |
| Energy Storage | $E = \frac{1}{2}CV^2$ (V is battery voltage) | $E = \frac{Q^2}{2C}$ (Q is the constant charge) |
In Summary
When a capacitor is charged by a battery and the battery is disconnected, the key outcome is that the electric charge accumulated on the capacitor's plates is isolated and remains constant. This allows the capacitor to act as an independent storage element for charge and energy, influencing its voltage and energy content based on its capacitance and any subsequent changes to its physical properties.
