The charging and discharging of a capacitor is a process by which charge is stored on or released from the capacitor's plates. The charging process is typically done by connecting the capacitor to a battery or other power source. The discharging process is typically done by connecting the capacitor to a resistor or other load.

&headingCharging process&heading

The charging process can be divided into two stages:

1. **The charging current stage:** In this stage, the capacitor is connected to a battery or other power source. The battery or power source provides a current that flows through the capacitor, charging the plates. The current in this stage is constant.
2. **The charging voltage stage:** In this stage, the capacitor is fully charged and the current stops flowing. The voltage across the capacitor plates is equal to the voltage of the battery or power source.

&headingDischarging process&heading

The discharging process can also be divided into two stages:

1. **The discharging current stage:** In this stage, the capacitor is connected to a resistor or other load. The resistor provides a path for the charge to flow out of the capacitor, discharging the plates. The current in this stage decreases exponentially.
2. **The discharging voltage stage:** In this stage, the capacitor is fully discharged and the voltage across the plates is zero.

Tip
Explaination

The mathematical expression for the growth of charge on the capacitor is:

Q = C(V_0 - V_t)

where:

* Q& is the charge on the capacitor (in coulombs)
* C is the capacitance of the capacitor (in farads)
* V_0 is the initial voltage across the capacitor (in volts)
* V_t is the voltage across the capacitor at time t (in volts)

&headingMathematical expression for the decay of charge on the capacitor&heading

The mathematical expression for the decay of charge on the capacitor is:

Q = Q_0 e^{-t/RC}

where:

* Q is the charge on the capacitor at time t (in coulombs)
* Q_0 is the initial charge on the capacitor (in coulombs)
* Rb is the resistance of the resistor (in ohms)
* C is the capacitance of the capacitor (in farads)
* t is the time (in seconds)

The diagram of the charging and discharging of a capacitor is shown below:

Diagram of the charging and discharging of a capacitor



The capacitor is represented by the two parallel plates. The battery or power source is represented by the symbol with the plus and minus signs. The resistor is represented by the zigzag line.

The charging process is shown by the arrow pointing from the battery to the capacitor. The discharging process is shown by the arrow pointing from the capacitor to the resistor.