Capacitors and Dielectrics: Storing Energy

Lesson 5 of 5: Electrostatics

In this lesson:

• Define capacitance and how capacitors store charge
• Calculate and
• Explain how dielectrics increase capacitance

What You Will Learn Today

By the end of this lesson, you will:

1. Define capacitance and explain what a capacitor does
2. Calculate using
3. Calculate energy stored:
4. Explain the role of a dielectric and how it increases
5. Describe practical applications of capacitors

Why Can't a Battery Power a Flash Directly?

• A flash needs massive energy in ~1 ms — more power than a battery can deliver
• Solution: charge a capacitor slowly, release all at once in the flash

Capacitor = energy reservoir — slow fill, fast release

A Capacitor: Two Plates, One Gap

• Two conducting plates separated by an insulating gap
• Connected to a source: on one plate, on the other
• Uniform between plates; disconnect → charge and field remain

Total charge = zero; the capacitor separates, not creates, charge

The Structure of a Parallel-Plate Capacitor

• on top plate, on bottom — equal and opposite
• Uniform between plates (from prior lesson on parallel plates)

Capacitors Are in Everything Around You

• Camera flash — stores energy slowly, releases in ~1 ms
• Defibrillator — delivers a high-energy pulse to the heart
• Computer RAM — tiny capacitors store bits (0 or 1)
• Power supplies — smooth voltage fluctuations

Same principle: store charge, release on demand

Check-In: Voltage Doubles — What Happens?

A capacitor switches from 6 V to 12 V.

What happens to the charge on each plate?

A) Stays the same — it's already charged

B) Doubles — more voltage draws more charge

C) Halves — voltage compresses charge

Think: what does voltage do to charge?

Answer: Charge Doubles with Voltage

Answer: B — Charge doubles

• Voltage is the "push" that drives charge onto the plates
• Double the voltage → double the charge stored
• This is the linear relationship that defines capacitance:

Capacitance Connects Charge to Voltage

• : charge stored (coulombs, C)
• : capacitance (farads, F); 1 F = 1 C/V
• : potential difference between plates (volts, V)
• Practical units: microfarads (F) or picofarads (pF)

C is a property of the geometry — not of Q or V alone

Capacitance Depends on Plate Geometry

• — permittivity of free space
• Larger → higher ; smaller → higher

Smaller gap: same → lower → larger

How Plate Geometry Changes Capacitance

• Larger : more surface area → more charge per volt → higher
• Smaller : shorter field path → same gives lower → higher

Worked Example: Find C and Then Q

, ,

Check-In: Effect of Halving the Gap

Capacitor: is reduced from 2 mm to 1 mm.

What happens to ?

A) halves — smaller gap, less space

B) doubles — in denominator → larger

C) stays the same — only matters

Apply

Answer: Smaller Gap Doubles Capacitance

Answer: B — doubles

• Smaller gap → same → smaller → higher
• This is why capacitors are built with very thin dielectrics (μm scale)

From Charge Storage to Energy Storage

• We can calculate and for any capacitor
• But capacitors store energy — that's what makes them useful
• How much energy is stored in the electric field between the plates?

The camera flash example will give us a real number — and a surprising one

Energy Stored in a Capacitor

• The factor: charging isn't done at constant voltage — it builds from 0 to ; average voltage is
• Energy is stored in the electric field between the plates

Three equivalent forms:

Three Equivalent Ways to Calculate Energy

• Convert between forms using
• Use whichever form matches the given quantities

If given and but not : use

If given and but not : use

Flash Capacitor: Energy and Power

• , :
• Released in 1 ms:

Check-In: Find Capacitance from Energy

A capacitor stores of energy at .

Find the capacitance .

Use , solve for

Try it before the next slide…

Answer: Rearranging the Energy Formula

• Rearrange first, then substitute numbers
• Unit check:

From Energy to the Field: Introducing Dielectrics

• Energy is stored in the field between the plates
• Can we store more energy without raising the voltage?
• Yes — insert a dielectric between the plates

Dielectric increases → more per volt → more stored energy

A Dielectric: Insulator That Boosts Capacitance

• Dielectric: insulator between the plates (plastic, ceramic, paper)
• Polar molecules align with field → opposing internal field forms
• Net field reduced → same , lower

Dielectric Polarization: How It Works

The dielectric reduces the net field — lower at same — higher

Dielectric Constant κ Multiplies Capacitance

• High field → dielectric breaks down → short circuit

Worked Example: Insert a Dielectric

, ; disconnected. Insert :

Key Takeaways: Capacitors and Dielectrics

✓ ; capacitance set by geometry:

✓ Energy stored:

✓ Dielectric inserts multiply by ; voltage drops

Watch Out: Three Capacitor Misconceptions

Capacitors ≠ batteries — fast release, not sustained current

Bigger : more charge at same , not higher

Dielectric lowers field and voltage — rises because falls

Chapter 18 Complete — What Comes Next

Chapter 19: Electric Current and Circuits

• Charge in motion → electric current
• Resistance and Ohm's Law:
• Capacitors in RC circuits: charge and discharge

from Lesson 4 is the same voltage that drives current