Question

Which variable of a capacitor Cannot change instantaneously?

Answer 1

In a capacitor, the voltage across the capacitor cannot change instantaneously. When a voltage is applied, it takes time for the charge to build up on the plates, and as a result, the voltage changes gradually according to the capacitor's time constant. This means that while the current can change instantaneously, the voltage across the capacitor cannot.

Answer 2

In a capacitor, the **voltage across the capacitor plates** cannot change instantaneously.

Here's a detailed explanation:

### Capacitor Basics

A capacitor is an electronic component that stores electrical energy in an electric field between two conductive plates separated by an insulating material (dielectric). The fundamental relationship governing a capacitor is given by:

\[ Q = C \cdot V \]

where:
- \( Q \) is the charge stored on the capacitor,
- \( C \) is the capacitance of the capacitor (which is constant for a given capacitor),
- \( V \) is the voltage across the capacitor.

### Voltage Behavior

The voltage across a capacitor is related to the charge on the capacitor by:

\[ V = \frac{Q}{C} \]

For a given capacitance \( C \), if the charge \( Q \) changes, the voltage \( V \) changes correspondingly.

### Instantaneous Changes

When considering instantaneous changes:

1. **Charge \( Q \)**: The charge on a capacitor can change almost instantaneously if there is a sudden change in the current supplied to the capacitor. For instance, if a capacitor is suddenly connected to a new voltage source, the charge will start to adjust to the new voltage over time.

2. **Voltage \( V \)**: According to the capacitor’s fundamental behavior, the voltage across the capacitor cannot change instantaneously because it would require an infinite current to do so. This is derived from the fact that the relationship between the current \( I \) flowing into a capacitor and the rate of change of voltage across it is given by:

   \[ I = C \cdot \frac{dV}{dt} \]

   For the voltage \( V \) to change instantaneously (i.e., with a very large \( \frac{dV}{dt} \)), the current \( I \) would need to be infinite, which is physically impossible in practical scenarios.

   Therefore, when the capacitor is subjected to a sudden change in the applied voltage, the voltage across it changes gradually, not instantaneously.

### Practical Implications

In practical circuits, this behavior means that capacitors are used to smooth out voltage changes and filter signals, as they resist sudden changes in voltage. This property is fundamental in applications such as power supply filtering, where capacitors help to maintain stable voltage levels.

In summary, the voltage across a capacitor is the variable that cannot change instantaneously due to the relationship between current and the rate of change of voltage.