A parallel-plate capacitor is charged by a 16.0 VV battery, then the battery is removed. What is the potential difference between the plates after the battery is disconnected?
The correct answer and explanation is:
Correct Answer:
The potential difference between the plates remains 16.0 V after the battery is disconnected.
Explanation:
A parallel-plate capacitor stores electric charge and energy when connected to a battery. When it is connected, the battery pushes electrons onto one plate and pulls them from the other, creating a separation of charge. This separation establishes an electric field between the plates, resulting in a potential difference equal to the battery’s voltage. In this case, the battery supplies 16.0 volts, so the capacitor’s plates reach a potential difference of 16.0 volts.
Once the battery is disconnected, the situation changes slightly but the potential difference stays the same. This happens because the plates are isolated conductors. The charge that was deposited on the plates has no external path to flow away; it is trapped unless there is a leakage path or a dielectric breakdown, which is not assumed here. The capacitance of the plates depends on physical properties like the area of the plates, the distance between them, and the material (dielectric) between them, but none of these properties change when the battery is removed.
The potential difference across the capacitor depends on the amount of charge and the capacitance according to the formula:
V=QCV = \frac{Q}{C}
The charge QQ remains constant because it has nowhere to go. The capacitance CC also stays constant unless something physically changes (like inserting or removing a dielectric or changing the plate separation). Since both QQ and CC stay the same, the potential difference VV must stay the same too.
Therefore, even though the battery is no longer connected, the plates retain their stored charge and the capacitor continues to hold a potential difference of 16.0 volts. This principle explains why capacitors can store energy and release it later in circuits, even after the charging source is removed.