Course: From Basic Science to Web Hosting

Module 01 — Basic Science

What Is Capacitance?

Difficulty: Beginner
Prerequisites: Lesson 006 — What Is Resistance?
Estimated time: 20 minutes

1. Learning Objectives

After this lesson, you should understand:

What capacitance is
What a capacitor is
How a capacitor stores energy
The relationship between charge and voltage
How a capacitor charges and discharges
What affects capacitance
Why capacitors are used in electronics
Why capacitance matters in computers and servers

2. Start With Electric Charge

We previously learned:

Electric charge
      ↓
Electric field
      ↓
Electric potential
      ↓
Voltage

Now ask:

Can we deliberately store electrical energy using an electric field?

Yes.

This is the basic idea behind a capacitor.

3. What Is a Capacitor?

A capacitor is an electrical component designed to store energy in an electric field.

A simple capacitor consists of two conductors separated by an insulating material.

Conceptually:

        Capacitor

      +++++++++++++
      +  Plate 1  +
      +++++++++++++
           │
       Insulator
           │
      -------------
      -  Plate 2  -
      -------------

The two conductive plates do not normally touch each other.

4. What Happens When We Connect a Battery?

Consider:

Battery
  │
  ├──── Capacitor ────┐
  │                   │
  └───────────────────┘

When connected, the battery causes charge separation on the capacitor plates.

Simplified:

Plate 1
++++++++++++

Plate 2
------------

This creates an electric field between the plates.

5. The Important Idea

A capacitor doesn’t simply “store electrons.”

More accurately:

A capacitor stores electrical energy in the electric field associated with separated charge.

The chain is:

Charge separation
      ↓
Electric field
      ↓
Stored electrical energy

6. What Is Capacitance?

Capacitance describes how much charge a capacitor stores for a given voltage.

The basic equation is:

C = Q/V

Therefore:

Q = CV

where:

C = capacitance
Q = charge
V = voltage

The unit of capacitance is the:

Farad (F)

7. Example

Suppose:

C = 1 F
V = 5 V

Then:

Q = CV

Q = 1 × 5

Q = 5 C

So the idealized capacitor stores 5 coulombs of charge separation at 5 V.

8. One Farad Is Large

A farad is a relatively large unit for many ordinary electronic circuits.

Common values include:

Microfarad     μF
Nanofarad      nF
Picofarad      pF

The relationships are:

1 μF = 10⁻⁶ F

1 nF = 10⁻⁹ F

1 pF = 10⁻¹² F

9. What Determines Capacitance?

For a simple parallel-plate capacitor:

C = εA/d

where:

C = capacitance
ε = permittivity of the material
A = plate area
d = separation between plates

Therefore:

Larger plate area
      ↓
Higher capacitance

and:

Smaller separation
      ↓
Higher capacitance

The dielectric material between the plates also affects capacitance.

10. Dielectric

The insulating material between capacitor plates is called the dielectric.

Examples include:

Ceramic
Plastic
Glass
Oxide layers

The dielectric changes the electric-field behavior between the plates and can increase capacitance compared with vacuum.

11. Capacitor Charging

Imagine an initially uncharged capacitor.

Time = 0

+ plate: 0
- plate: 0

Connect a voltage source.

Initially, charge begins accumulating on the plates.

Start
 ↓
Charge separation increases
 ↓
Voltage across capacitor increases
 ↓
Eventually approaches source voltage

For a simple resistor-capacitor circuit:

Battery ── R ── C

the charging is not instantaneous.

12. Why Doesn’t It Charge Instantly?

The resistor limits current.

So:

Resistance
     +
Capacitance
     ↓
Charging takes time

This leads to an important concept:

Time Constant

For a simple RC circuit:

τ = RC

where:

τ = time constant
R = resistance
C = capacitance

13. Example

Suppose:

R = 1 kΩ
C = 100 μF

Then:

τ = RC

Convert:

R = 1000 Ω
C = 100 × 10⁻⁶ F

Therefore:

τ = 1000 × 100 × 10⁻⁶
τ = 0.1 s

So the time constant is:

100 ms

14. What Does One Time Constant Mean?

For a simple charging capacitor, after approximately one time constant:

~63%

of the final voltage has been reached.

After approximately:

1τ → 63%
2τ → 86%
3τ → 95%
4τ → 98%
5τ → 99%+

So after roughly five time constants, the capacitor is very close to its final voltage.

15. Capacitor Discharging

Now imagine a charged capacitor connected through a resistor.

Capacitor
    ↓
Resistor
    ↓
Discharge

The stored energy is released through the circuit.

The voltage decreases exponentially:

High voltage
     │\
     │ \
     │  \
     │   \
     │    \____
     └──────────── Time

Again, the time constant is:

τ = RC

16. Capacitor Energy

The energy stored in an ideal capacitor is:

E = ½CV²

where:

E = energy in joules
C = capacitance
V = voltage

Notice that energy depends on voltage squared.

So increasing voltage can significantly increase stored energy.

17. Example

Suppose:

C = 1000 μF
V = 10 V

Convert:

C = 0.001 F

Then:

E = ½CV²

E = ½ × 0.001 × 10²

E = 0.05 J

The capacitor stores approximately:

0.05 joule

in the idealized case.

18. Does Current Flow Through a Capacitor?

This is an important question.

In a simple DC steady-state circuit, an ideal capacitor eventually behaves like an open circuit.

But during charging or discharging, current flows in the external circuit.

For a capacitor:

i = C(dV/dt)

Therefore:

Voltage changing rapidly
       ↓
Larger capacitor current

and:

Voltage constant
       ↓
Ideal capacitor current = 0

for steady-state DC.

19. Capacitor and DC

Suppose we connect a capacitor to a DC battery.

Initially:

Current flows

As the capacitor charges:

Current decreases

Eventually:

Current → 0

for an ideal capacitor under steady DC conditions.

So:

DC
 ↓
Capacitor
 ↓
Transient current
 ↓
Steady state → no ideal current

20. Capacitor and Changing Signals

Capacitors behave differently when voltage is continuously changing.

This makes them useful in:

Filters
Signal coupling
Timing circuits
Oscillators
Power supplies
Noise suppression
Memory circuits

21. Capacitors in Power Supplies

Electronic devices need stable power.

A simplified power supply might contain:

AC
 ↓
Rectifier
 ↓
Pulsating DC
 ↓
Capacitor
 ↓
Smoother DC
 ↓
Regulator
 ↓
Electronic circuit

The capacitor helps reduce voltage fluctuations.

22. Capacitors in Computers

Computers contain enormous numbers of capacitive effects.

Capacitance exists in:

Transistors
Interconnects
Circuit nodes
Memory cells
Input/output structures

These capacitances affect how quickly electronic signals can change.

For example:

Transistor switches
       ↓
Capacitive load must charge/discharge
       ↓
Signal transition takes time
       ↓
Limits switching speed

This is one reason capacitance matters to CPU performance.

23. Capacitors and Digital Signals

A digital signal may look like:

High ────────┐      ┌────────
             │      │
             │      │
Low          └──────┘

But a real signal cannot change infinitely fast.

Because of circuit resistance and capacitance:

Ideal:

      ┌──────
      │
──────┘

Real:

      /──────
     /
─────

The transition has a finite rise/fall time.

24. Resistance + Capacitance

We now have two important electrical properties:

Resistance
    ↓
Opposes current / dissipates energy

Capacitance
    ↓
Stores energy in an electric field

Together:

R + C
 ↓
RC circuit
 ↓
Timing
Filtering
Signal shaping

25. From Capacitor to Computer

Our technology chain is becoming deeper:

Matter
 ↓
Atoms
 ↓
Electrons
 ↓
Charge
 ↓
Electric field
 ↓
Voltage
 ↓
Current
 ↓
Circuit
 ↓
Resistance
 ↓
Capacitance
 ↓
Electronic circuits
 ↓
Semiconductors
 ↓
Transistors
 ↓
Digital electronics
 ↓
Computer

Eventually:

Computer
 ↓
Operating System
 ↓
Networking
 ↓
Internet
 ↓
Web Server
 ↓
Web Hosting

26. Quick Check

What does a capacitor store?

Electrical energy in an electric field.