The Relation between Current and Voltage in a Capacitor

The relation between current and voltage in a capacitor can be described by the equation: I = CdV/dt, which is represented by option 'B' in the given choices.

Explanation:

Capacitance:
A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material known as a dielectric. The ability of a capacitor to store charge is quantified by its capacitance, denoted by the symbol 'C'. The unit of capacitance is the Farad (F).

Voltage across a Capacitor:
When a voltage is applied across the plates of a capacitor, it creates an electric field between the plates. This electric field causes charge to accumulate on the plates, resulting in a voltage across the capacitor. The voltage across a capacitor is denoted by 'V'.

Current through a Capacitor:
When the voltage across a capacitor changes, the charge on the plates also changes. This change in charge over time gives rise to an electric current flowing through the capacitor. The current through a capacitor is denoted by 'I'.

Relation between Current and Voltage:
The equation that relates the current through a capacitor to the voltage across it is given by I = CdV/dt.

- 'C' represents the capacitance of the capacitor, which is a constant value.
- 'dV/dt' represents the rate of change of voltage with respect to time.

This equation indicates that the current flowing through a capacitor is directly proportional to the rate of change of voltage across it. In other words, the faster the voltage across the capacitor changes, the larger the current flowing through it.

It is important to note that the integral of current with respect to time gives the net charge stored in the capacitor: Q = ∫Idt. This relationship can be derived from the equation I = CdV/dt by integrating both sides with respect to time.

Therefore, the correct option that represents the relation between current and voltage in a capacitor is 'B': I = CdV/dt.