The process of charging and discharging a capacitor involves the flow of electric charge between the capacitor’s plates. Capacitors store electrical energy in an electric field created by separated charges on the capacitor plates. Here’s a detailed explanation of how a capacitor gets charged and discharged:

### 1. **Charging a Capacitor:**

**Voltage Source Connection:**- To charge a capacitor, it needs to be connected to a voltage source, such as a battery or power supply. The voltage source provides an electric potential difference (voltage) across the capacitor terminals.

**Initial State:**- Initially, when the capacitor is uncharged, both plates have an equal number of electrons, resulting in a neutral overall charge.

**Connecting to Voltage Source:**- When the capacitor is connected to the voltage source, electrons on one plate are repelled by the negative terminal of the source and attracted to the positive terminal. Simultaneously, electrons from the other plate are attracted to the negative terminal. This movement of electrons creates an excess of negative charge on one plate and an equal positive charge on the other.

**Electric Field Formation:**- As charge accumulates on the capacitor plates, an electric field develops between the plates. This electric field opposes the continued flow of electrons, creating a potential difference that eventually reaches equilibrium with the voltage of the source.

**Charging Current:**- Initially, the current flowing into the capacitor is at its maximum, but as the voltage across the capacitor approaches that of the voltage source, the charging current decreases. The charging process continues until the voltage across the capacitor matches the voltage of the source.

**Capacitor Voltage-Time Relationship:**- The voltage across the capacitor during charging follows an exponential growth curve described by the formula V(t) = V₀(1 – e^(-t/RC)), where V(t) is the voltage at time t, V₀ is the final voltage, R is the resistance in the circuit, and C is the capacitance of the capacitor.

### 2. **Discharging a Capacitor:**

**Disconnecting from Voltage Source:**- To discharge a capacitor, it needs to be disconnected from the voltage source. Once disconnected, the capacitor retains the charge it accumulated during the charging process.

**Connecting to a Load:**- When a capacitor is connected to a resistor or any load in a circuit, the stored charge begins to flow through the circuit. The capacitor discharges through the load, providing an electric current.

**Discharge Current:**- The discharge current follows an exponential decay curve as the charge on the capacitor decreases over time. The rate of discharge is influenced by the resistance in the circuit and the capacitance of the capacitor.

**Voltage Decay:**- The voltage across the capacitor decreases during discharge, following the exponential decay formula V(t) = V₀ * e^(-t/RC), where V(t) is the voltage at time t, V₀ is the initial voltage across the capacitor, R is the resistance, and C is the capacitance.

**Time Constant:**- The time constant (τ) of the RC circuit, given by the product of resistance (R) and capacitance (C), determines the rate of charging or discharging. A larger time constant results in slower changes in voltage, while a smaller time constant leads to faster changes.

### 3. **Energy Storage and Release:**

**Energy Transfer:**- Charging and discharging involve the transfer of electrical energy between the capacitor plates and the surrounding circuit. During charging, energy is stored in the electric field between the plates, and during discharging, this stored energy is released as electric current flows through the circuit.

### 4. **Applications:**

**Timing Circuits:**- Capacitors are often used in timing circuits, where the charging and discharging processes determine the timing intervals. The time constant of an RC circuit can be manipulated for specific applications.

**Signal Filtering:**- In electronic circuits, capacitors are used for signal filtering. They can store and release charge to smooth out variations in voltage, reducing noise or ripple in the signal.

**Energy Storage:**- Capacitors serve as energy storage devices in various electronic systems. They can quickly release stored energy when needed, making them suitable for applications like flash photography in cameras.

In summary, charging a capacitor involves connecting it to a voltage source, leading to the accumulation of charge on its plates and the creation of an electric field. Discharging occurs when the capacitor is connected to a load, allowing the stored charge to flow through the circuit. The charging and discharging processes are fundamental to the operation of capacitors in electronic circuits and find applications in diverse areas of electronics and technology.