A capacitor is an electronic component that stores and releases electrical energy. It consists of two conductive plates separated by an insulating material (dielectric), creating an electric field between them. When a voltage is applied across the plates, one plate accumulates positive charge while the other accumulates negative charge, creating a potential difference.
Capacitance is the measure of a capacitor’s ability to store electric charge when a potential difference is applied across its plates.
The capacitance (C) of a parallel plate capacitor is given by the formula:
\begin{equation} C = \frac{Q}{V} = \frac{E_0 \cdot A}{d} \end{equation}
\begin{equation} \text{Capacitance} = \frac{\text{Magnitude of charge on Conductor}}{\text{Magnitude of potential difference}} \end{equation}
Capacitors can be combined in parallel or in series to achieve different effective capacitance values.
In a parallel combination, the positive plates of all capacitors are connected together, and the negative plates are also connected together.
Let’s suppose a capacitor consists of such a combination that the positive terminal of each capacitor is connected with the positive terminal of the other capacitor and the negative terminal of each capacitor is connected with the negative terminal of the other capacitor. Then the combination is said to be a Parallel combination.
If three Capacitors C1, C2, and C3 are connected in Parallel and further connected with a battery of V volts then: C₁ draws charge Q1, C2 draws charge Q2 and C3 draws charge Q3.
Then:
Q = Q1 + Q₂+Q3.
By applying the Capacitor equation. We get:
Q1=C₁V, Q2=C2V, Q3=C3V, Q= C0V
So capacitance becomes:
CeV=C₁V+C₂V+C3V
CeV = (C1+C₂+ C3) V
Ce=C1+C2+ C3
In a series combination, the positive plate of one capacitor is connected to the negative plate of the next capacitor, forming a chain.
Let suppose Capacitors are consists on such a combination that positive terminal of one Capacitor connected with the negative terminal of the other Capacitor and the negative terminal of first Capacitor is connected with the positive terminal of the other Capacitor.
Then the combination is said to be Series combination.
If three Capacitor C1, Cz and C3 are connected in Series and further connects them with a battery of V volts.
Then: Positive plate of Capacitor C1 draws charge +Q from the battery ad negative plate of C3 draws charge – Q from the battery.
The charge +Q on the positive terminal (Left Plate) of Ci attracts free electrons from the left plate of Cz and these free electrons are accumulated on the right plate of C1. Thus right plate of C₁ becomes negatively charged with a charge-Q. in this way every Capacitor becomes charged. If voltage acquired by each Capacitor is V1, V2, V3 by applying Capacitor equation on C1, C2 and C3. We get:
Q= C1V1, Q= C2V2, Q= C3V3, Q=CeV
\begin{align} V_1 &= \frac{Q}{C_1} \\ V_2 &= \frac{Q}{C_2} \\ V_3 &= \frac{Q}{C_3} \end{align}
\begin{equation} \frac{Q}{C_e} = Q \left(\frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}\right) \end{equation}
\begin{equation} \frac{1}{C_e} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \end{equation}
So now according to the equation:
The reciprocal of equivalent capacitance is equal to the sum of reciprocals of individual capacitance.
Capacitors have various applications across multiple fields. Some of their uses include:
Capacitors store electrical energy and provide quick bursts of power, making them essential components in flashlights, camera flashes, and defibrillators.
Capacitors are employed in tuning radio receivers, antennas, and circuits to resonate at specific frequencies, optimizing performance.
Capacitors are used in split-phase and capacitor-start motors to control phase relationships and starting performance.
Capacitors stabilize voltage levels, reduce voltage fluctuations, and prevent voltage spikes in electronic systems.
Capacitors serve as charge storage elements in dynamic random-access memory (DRAM) chips, used in computers and digital devices.
Capacitors play a role in NAND flash memory cells, storing data in devices like USB drives, SSDs, and memory cards.