1. Concept Overview
Capacitance describes how well a conductor can store electric charge. Whenever two conductors are separated by an insulator (air, vacuum, or any dielectric), they can hold charge in a controlled way. This ability to store charge and energy makes capacitors one of the most useful electrical components.
2. Definition
Capacitance is the ratio of the charge stored on a conductor to the potential difference applied across it.
Mathematically:
\( C = \dfrac{Q}{V} \)
It tells how much charge \( Q \) is stored per volt of potential difference \( V \).
3. Unit of Capacitance
The SI unit of capacitance is the farad (F).
3.1. Smaller Units
- Microfarad (µF) = \(10^{-6}\) F
- Nanofarad (nF) = \(10^{-9}\) F
- Picofarad (pF) = \(10^{-12}\) F
Most practical capacitors are measured in these smaller units because one farad is a very large value.
4. Parallel Plate Capacitor
The simplest and most widely used capacitor model consists of two parallel conducting plates separated by an insulator. Its capacitance can be calculated using geometry.
4.1. Formula
For two plates of area \( A \) separated by distance \( d \):
\( C = \dfrac{\varepsilon_0 A}{d} \)
This formula assumes air or vacuum between the plates.
4.2. Interpretation
- Larger plate area → more charge can be stored → higher capacitance.
- Smaller separation → stronger interaction between plates → higher capacitance.
5. Effect of Dielectric
Placing an insulating material (dielectric) between the plates increases capacitance. The dielectric reduces the effective electric field inside the capacitor, allowing more charge to be stored for the same potential difference.
5.1. Formula with Dielectric
\( C = \kappa \dfrac{\varepsilon_0 A}{d} \)
where \( \kappa \) is the dielectric constant of the material.
5.2. Interpretation
A higher dielectric constant makes it easier to store charge. Materials like glass, mica, or ceramics significantly increase capacitance.
6. Charge–Voltage Relationship
The relationship \( C = Q/V \) means that for a fixed capacitance, the stored charge increases as potential increases. On a graph, \( Q \) vs. \( V \) is a straight line with slope equal to capacitance.
7. Energy Stored in a Capacitor (Intro Only)
A charged capacitor stores energy in the electric field between its plates. The energy is given by:
\( U = \dfrac{1}{2}CV^2 \)
This idea is used later in detail.
8. Key Factors Affecting Capacitance
- Plate area \( A \)
- Distance between plates \( d \)
- Dielectric constant \( \kappa \)
- Geometry of conductors
9. Worked Examples
9.1. Example 1: Capacitance Calculation
Two plates each of area \( 0.4 \text{ m}^2 \) are separated by \( 2 \times 10^{-3} \text{ m} \). The capacitance is:
\( C = \dfrac{\varepsilon_0 A}{d} = \dfrac{8.85 \times 10^{-12} \times 0.4}{2 \times 10^{-3}} = 1.77 \times 10^{-9} \text{ F} = 1.77 \text{ nF} \).
9.2. Example 2: Adding a Dielectric
If a dielectric with \( \kappa = 5 \) is inserted into the same capacitor:
\( C = 5 \times 1.77 \text{ nF} = 8.85 \text{ nF} \).
The capacitance increases five times.
10. Physical Interpretation
You can think of capacitance as the “capacity to hold charge.” Larger plates or closer spacing help store more charge. Inserting a dielectric acts like giving the capacitor more room to store energy by reducing the effective electric field inside. Almost every electronic device uses capacitors for energy storage, signal filtering, timing circuits and many other applications.