Capacitors

Learning Objectives

By the end of this page, you should be able to:

• Define capacitance and explain how a capacitor stores energy in an electric field
• Calculate charge, voltage, and stored energy using Q = CV and E = ½CV²
• Distinguish ceramic, electrolytic, film, variable, and super capacitors by construction and typical use
• Explain the RC charging/discharging curve and calculate the time constant τ = RC
• Describe how capacitors behave differently at DC and AC, and why this makes them useful for filtering and coupling
• Identify at least four practical circuit applications of capacitors

Quick Answer

A capacitor is a passive two-terminal component that stores electrical energy in an electric field between two conductive plates separated by an insulating dielectric. Its capacitance, measured in farads, tells you how much charge it stores per volt applied: Q = CV. Capacitors block steady DC once charged but let AC signals pass, which is why they show up everywhere — smoothing ripple in power supplies, coupling audio signals between amplifier stages, filtering noise, and setting the timing of oscillators. The type of capacitor you choose (ceramic, electrolytic, film) depends on the capacitance value needed, the voltage rating, and whether polarity matters.

What Is a Capacitor?

A capacitor consists of two conductive plates separated by a thin insulating layer called a dielectric — this might be air, ceramic, plastic film, or an oxide layer. When you connect a voltage source across the plates, electrons pile up on one plate and are pulled away from the other, creating an electric field across the dielectric. That field is where the energy lives. Unlike a resistor, a capacitor does not dissipate energy as heat (ideally) — it stores it and can give it back later.

The amount of charge a capacitor can hold per volt is its capacitance, C, measured in farads (F). Since a farad is a huge unit for most electronics work, you will mostly see microfarads (µF), nanofarads (nF), and picofarads (pF).

Q = C × V

Where:

• Q is the stored charge (coulombs)
• C is the capacitance (farads)
• V is the voltage across the capacitor (volts)

Capacitance itself depends on the physical construction:

C = ε × A / d

Where ε is the permittivity of the dielectric, A is the plate area, and d is the distance between plates. Bigger plates or a thinner dielectric means more capacitance; a better (higher-permittivity) dielectric material also increases it.

How Capacitors Charge and Discharge

When you connect a capacitor to a DC source through a resistor, current does not jump straight to zero or full value — it follows an exponential curve. This is the defining behaviour that makes capacitors useful for timing circuits.

• Charging: Current is highest the instant voltage is applied (the capacitor looks like a short circuit when empty) and decays as the capacitor fills up. Voltage across the capacitor rises from 0 toward the supply voltage.
• Discharging: When the source is removed and a path is provided, the stored charge flows back out, with voltage decaying exponentially toward zero.

The speed of this charging/discharging is set by the time constant:

τ = R × C

After one time constant, the capacitor reaches about 63% of the target voltage (charging) or falls to about 37% of its starting voltage (discharging). After roughly five time constants, it is considered fully charged or discharged for practical purposes.

The energy stored in a charged capacitor is:

E = ½ × C × V²

This is why capacitors — especially supercapacitors — are used for short-term energy storage: they release stored energy fast, unlike a battery's slower chemical reaction.

Types of Capacitors

Ceramic Capacitors

Made from a ceramic dielectric, these are cheap, small, and non-polarized. They cover a wide range from a few picofarads to several microfarads and are the default choice for bypassing and decoupling noise near IC power pins.

Electrolytic Capacitors

These use a thin oxide layer as the dielectric, which lets them pack much higher capacitance (microfarads to farads) into a small volume. The tradeoff is that they are polarized — connect one backwards and it can leak, bulge, or in a bad case burst. They are the standard choice for smoothing the ripple in a rectified power supply.

Film Capacitors

Built with a plastic film dielectric (polyester, polypropylene), these have low loss, good stability over temperature, and no polarity to worry about. They are preferred in precision analog circuits, audio crossover networks, and timing circuits where accuracy matters more than compact size.

Variable Capacitors

Mechanically or electronically adjustable capacitance, historically used to tune the resonant frequency of a radio receiver by turning a dial that changes plate overlap area.

Supercapacitors

Also called ultracapacitors, these achieve enormous capacitance (farads to thousands of farads) using a different charge-storage mechanism (electric double-layer) rather than a simple dielectric. They cannot store as much total energy as a battery of the same size, but they charge and discharge far faster and survive far more cycles — useful for regenerative braking energy capture and providing burst power in hybrid vehicles.

Capacitors at DC vs AC

A capacitor's opposition to current — its reactance — depends on frequency:

X_C = 1 / (2πfC)

At DC (f = 0), reactance is infinite: once charged, no current flows, so a capacitor blocks DC. At high frequencies, reactance drops toward zero, so a capacitor looks almost like a short circuit to fast-changing signals. This single fact explains most capacitor applications:

• Coupling: A capacitor between amplifier stages passes the AC audio signal while blocking the DC bias voltage of each stage from interfering with the next.
• Decoupling/bypassing: A capacitor near an IC's power pin shunts high-frequency switching noise to ground while leaving the steady DC supply untouched.
• Filtering: In a power supply, a large capacitor across the rectified DC output smooths the ripple because it charges on the peaks and supplies current during the dips.

Real-World Example

A phone charger converts mains AC into DC. After rectification the voltage still has ripples riding on it, twice per mains cycle. A large electrolytic capacitor (typically 100–1000 µF) is placed across the output — it charges up on each ripple peak and discharges slightly between peaks, flattening the output into something close to steady DC that a linear regulator can clean up further.

Applications of Capacitors

• Power supply filtering: Smoothing ripple after rectification
• Coupling: Passing AC signals between amplifier stages while blocking DC
• Decoupling/bypassing: Suppressing high-frequency noise near ICs
• Timing: Setting RC time constants in oscillators and 555 timer circuits
• Energy storage: Supercapacitors for burst power and backup memory retention

Practical Circuit Example: RC Low-Pass Filter

Placing a resistor in series with the input and a capacitor from the output node to ground creates a low-pass filter: high-frequency signals see a low-reactance path to ground through the capacitor and are attenuated, while low-frequency and DC signals pass through relatively unaffected. The cutoff frequency is f = 1 / (2πRC).

---

Key Terms

Term	Definition	Related Concept
Capacitance	Ability to store charge per volt, measured in farads (F)	Q = CV
Dielectric	Insulating material between capacitor plates	Ceramic, film, oxide layer
Time constant (τ)	Time for charge/discharge to reach ~63%/37% of final value; τ = RC	RC circuits
Reactance (X_C)	Opposition to AC current, X_C = 1/(2πfC), frequency-dependent	Filtering
Electrolytic capacitor	Polarized capacitor using an oxide dielectric for high capacitance	Power supply filtering
Ceramic capacitor	Non-polarized capacitor for small values and decoupling	IC bypassing
Supercapacitor	Very high capacitance device using electric double-layer storage	Burst energy storage
Coupling capacitor	Passes AC signal, blocks DC between circuit stages	Amplifier design
Ripple voltage	Residual AC variation on a rectified DC supply	Power supply design
Working voltage	Maximum voltage a capacitor can safely withstand	Component derating

Common Mistakes

Misconception: A capacitor with a larger capacitance value is always "better" for a given circuit. Why it's wrong: Capacitance value must match the function. A large electrolytic capacitor used for high-frequency decoupling actually performs poorly because its internal inductance (ESL) makes it a bad short at high frequencies — small ceramic capacitors are better there. Correct understanding: Match the capacitor type and value to the frequency and function: small ceramics for high-frequency decoupling, larger electrolytics for bulk low-frequency filtering.

---

Misconception: Any capacitor can be connected either way round in a circuit. Why it's wrong: Electrolytic and tantalum capacitors are polarized. Reverse-biasing them can break down the internal oxide dielectric, causing excessive leakage current, heating, and in the worst case a burst capacitor. Correct understanding: Always check the polarity markings (the stripe or longer lead) on electrolytic and tantalum capacitors before connecting them; ceramic and film capacitors are typically non-polarized.

---

Misconception: A charged capacitor with no visible connections is automatically safe to touch. Why it's wrong: Large capacitors, especially in power supplies and camera flash circuits, can hold a lethal or damaging charge for a long time after power is removed if there's no discharge path. Correct understanding: Always discharge large capacitors through an appropriate resistor before handling a circuit, even after switching off the power.

Comparison and Connections

Feature	Ceramic	Electrolytic	Film	Supercapacitor
Polarity	Non-polarized	Polarized	Non-polarized	Polarized
Typical range	pF to a few µF	µF to mF	nF to µF	F to thousands of F
Best for	High-frequency decoupling	Bulk power filtering	Precision timing, audio	Burst energy, backup power
Stability	Moderate (varies with type)	Lower, degrades with age	High	N/A (different mechanism)
Typical failure mode	Cracking (mechanical stress)	Drying out, bulging	Rare, very reliable	Capacity fade over cycles

Practice Questions

Recall

1. What is the formula relating charge, capacitance, and voltage? Answer guidance: Q = C × V.

2. Name three common dielectric materials used in capacitors. Answer guidance: Ceramic, plastic film (polyester/polypropylene), and the oxide layer used in electrolytic capacitors (also air, mica, tantalum oxide).

Understanding

3. Why does a capacitor block DC but pass AC? Answer guidance: Reactance X_C = 1/(2πfC). At DC, f = 0, so X_C is infinite and no steady current flows once charged. At higher frequencies, X_C decreases, so AC signals pass more easily.

4. Why must electrolytic capacitors be connected with correct polarity, while ceramic capacitors need not be? Answer guidance: Electrolytic capacitors rely on a thin oxide layer formed by the correct polarity to act as the dielectric; reverse voltage breaks this layer down. Ceramic capacitors use a symmetric solid dielectric with no polarity dependence.

Application

5. A 100 µF capacitor is charged through a 1 kΩ resistor from a 10 V supply. What is the time constant, and what is the voltage across the capacitor after one time constant? Answer guidance: τ = RC = 1000 × 100×10⁻⁶ = 0.1 s. After one time constant, voltage ≈ 63% of 10 V = 6.3 V.

6. You need to filter high-frequency switching noise near a microcontroller's power pin. Which type of capacitor and approximate value would you choose, and why? Answer guidance: A ceramic capacitor, typically 0.1 µF (100 nF), placed as close as possible to the power pin — ceramics have low ESL/ESR, making them effective at high frequencies where noise occurs.

Analysis

7. Two capacitors, 10 µF and 20 µF, are connected in parallel, then separately in series. Calculate the equivalent capacitance for each case and explain the physical reason for the difference. Answer guidance: Parallel: C = 10 + 20 = 30 µF (effectively increases plate area). Series: 1/C = 1/10 + 1/20 = 3/20, so C ≈ 6.67 µF (effectively increases plate separation, reducing capacitance).

8. A power supply's output ripple increases noticeably after years of use, even though the load hasn't changed. What is the likely cause and why? Answer guidance: Electrolytic capacitors dry out over time as their electrolyte evaporates, reducing effective capacitance and increasing equivalent series resistance (ESR). Both effects reduce filtering effectiveness and increase ripple.

FAQ

What's the difference between capacitance and charge? Charge (Q, in coulombs) is the actual amount of stored electric charge at a given voltage. Capacitance (C, in farads) is a fixed property of the component describing how much charge it stores per volt applied. A bigger capacitor stores more charge at the same voltage, but charge also depends on the voltage applied — double the voltage and you double the stored charge for the same capacitor.

Why do power supplies use such large capacitor values (like 1000 µF) while signal circuits use tiny values (like 10 pF)? It comes down to function and frequency. Power supply filtering needs to smooth relatively slow, low-frequency ripple (100–120 Hz), which requires large capacitance to store enough charge between ripple peaks. High-frequency signal or timing circuits operate at much higher frequencies, where even a small capacitance provides sufficient reactance to do the job — and smaller capacitors respond faster with less parasitic inductance.

Can a capacitor actually explode? Yes, mainly electrolytic capacitors. If reverse-biased, over-voltaged, or if the electrolyte degrades and produces gas faster than a vent can release it, pressure builds until the case ruptures. Most modern electrolytics have a scored top that vents gas before a violent explosion, but they can still pop loudly and spray hot electrolyte.

How is a supercapacitor different from a battery? A battery stores energy through a reversible chemical reaction, giving high energy density but slower charge/discharge and a limited number of cycles. A supercapacitor stores energy physically in an electric field (like a regular capacitor but with a huge effective surface area), giving lower energy density but very fast charge/discharge and hundreds of thousands of cycles without significant degradation.

Why do some capacitors have a minus sign and a stripe on one side? That marks the negative terminal of a polarized capacitor (usually electrolytic or tantalum). The stripe (often with a minus sign) tells you which lead must be connected to the lower-voltage side of the circuit. Getting it backwards is one of the most common beginner circuit mistakes.

Quick Revision

• A capacitor stores energy in an electric field between two plates separated by a dielectric
• Q = CV relates charge, capacitance, and voltage
• Energy stored: E = ½CV²
• Time constant τ = RC governs charging/discharging speed; ~63% charged after one τ
• Capacitive reactance X_C = 1/(2πfC) — decreases as frequency increases
• Capacitors block DC (once charged) and pass AC — the basis of coupling and filtering
• Electrolytic capacitors are polarized and give high capacitance in small volume; watch polarity
• Ceramic capacitors are non-polarized, best for high-frequency decoupling
• Film capacitors offer stability and precision for timing and audio
• Supercapacitors give very high capacitance for fast, high-cycle-count energy storage
• Series capacitors: 1/Ctotal = 1/C1 + 1/C2 (decreases); Parallel capacitors: Ctotal = C1 + C2 (increases)

Related Topics

Prerequisites: Electric charge and electric fields; Ohm's law; basic circuit concepts; resistors

Related Topics: Resistors (RC timing and filter circuits); inductors (LC resonant circuits); rectifier and power supply design; oscillator circuits

Next Topics: Inductors; RC and LC filter design; power supply rectification and regulation; transistor coupling networks