Capacitor Charge Calculator — Energy, Charge, Voltage & RC Circuit

Physics — Electricity & Circuits

Capacitor Charge Calculator

Q: What is the formula for energy stored in a capacitor?

There are three equivalent formulas for energy stored in a capacitor: E = ½CV² (most common, using capacitance and voltage), E = Q²/(2C) (using charge and capacitance), and E = ½QV (using charge and voltage). All three give identical results. For example, C=100μF at V=12V: E = ½ × 100×10⁻⁶ × 144 = 7.2×10⁻³ J = 7.2 mJ.

Q: How do you calculate capacitor charge?

Use the capacitor charge formula Q = C × V, where Q is charge in Coulombs, C is capacitance in Farads, and V is voltage in Volts. Example: C=100μF=100×10⁻⁶ F at V=12V gives Q = 100×10⁻⁶ × 12 = 1.2×10⁻³ C = 1.2 mC. Always convert capacitance to Farads before calculating.

Q: What is the time constant of an RC circuit?

The time constant τ = RC (resistance × capacitance) is the time for a discharging capacitor to fall to 36.8% (1/e) of its initial voltage, or for a charging capacitor to reach 63.2% of the supply voltage. After 5τ, the capacitor is considered fully discharged (0.67% remaining) or fully charged (99.33%). Example: R=10kΩ, C=470μF → τ = 10000 × 470×10⁻⁶ = 4.7 seconds.

Q: What is the difference between series and parallel capacitors?

Parallel capacitors: C_total = C₁ + C₂ + ... (total is greater than the largest — adds plate area). Series capacitors: 1/C_total = 1/C₁ + 1/C₂ + ... (total is less than the smallest — equivalent to increasing plate separation). For two capacitors in series: C_total = C₁C₂/(C₁+C₂). This is opposite to resistors: capacitors in series give less capacitance (like resistors in parallel give less resistance).

Q: Why does the energy formula for a capacitor have a ½ factor?

The ½ factor arises because as the capacitor charges, the voltage increases from 0 to V — the average voltage during charging is V/2, not V. Mathematically: E = ∫₀Q (Q'/C) dQ' = Q²/2C = ½CV². If you used CV² instead of ½CV², you would overestimate the stored energy by a factor of 2. The other half of the energy supplied by the source is dissipated as heat in the series resistance.

Q: What is a Farad?

A Farad (F) is the SI unit of capacitance. 1 Farad = 1 Coulomb per Volt. A capacitor of 1 Farad stores 1 Coulomb of charge when 1 Volt is applied across it. One Farad is an enormous capacitance — a parallel plate capacitor with 1mm air gap would need ~9×10¹² m² of plate area to achieve 1 Farad. In practice, capacitors range from picofarads (pF = 10⁻¹² F) for RF circuits to thousands of microfarads (μF = 10⁻⁶ F) for power supplies.

Q: How long does it take a capacitor to fully discharge?

Theoretically, a capacitor never fully discharges (the exponential V = V₀e^(-t/RC) never reaches zero). In practice, after 5τ = 5RC, the voltage is only 0.67% of its initial value, which is considered fully discharged. For example: C=470μF, R=10kΩ → τ=4.7s → fully discharged after 5τ = 23.5 seconds. The time to reach any specific voltage is t = -τ × ln(V_target/V₀).

Calculates the energy stored in a capacitor using all three equivalent formulas (E=½CV², E=Q²/2C, E=½QV), finds charge and voltage from capacitance, and solves RC circuit charging and discharging problems — using the energy stored in capacitor formula with full step-by-step working throughout.

E = ½CV² Q = CV τ = RC E = Q²/2C

Capacitor Charge Calculator

Select which two values you know:

🔊 Car audio cap: 100μF, 12V

⚡ Power supply: 1000μF, 5V

📡 Signal: 10nF, 100V

🔋 Supercap: 1F, 2.7V

📷 Flash cap: E=1J, V=400V

Capacitance (C)

Voltage (V)

Charge (Q)

Energy (E)

Error

Capacitance

—

Voltage

—

Charge

—

Energy Stored

—

Three Equivalent Energy Formulas — All Verified

E = ½CV² — ✓

E = Q²/(2C) — ✓

E = ½QV — ✓

Step-by-Step Working

⏱ Timing: 470μF, 10kΩ

🔌 Filter: 100μF, 1kΩ

🎯 Precision: 1μF, 1MΩ

📷 Flash: 100μF, 10Ω, 300V

Initial voltage V₀

Resistance (R)

Capacitance (C)

Time of interest (t)

Find Time for Target Voltage (optional)

Error

Time	Discharge V(t)	Charge V(t)	% (Dis)	Status

Step-by-Step RC Working

C₁

C₂

Applied voltage (for charge/energy calculation)

Error

Step-by-Step

Parallel Plate Capacitor Formula

C = ε₀ × εᵣ × A / d

ε₀ = 8.854×10⁻¹² F/m | εᵣ = dielectric constant

Plate area (A)

Plate separation (d)

Applied voltage (optional — for E-field & energy)

Dielectric material

Custom εᵣ:

Error

Step-by-Step

Table A — Three Equivalent Energy Formulas for a Capacitor

Formula	When to Use	Derivation
E = ½CV²	C and V known — most common form	E = ∫₀Q (Q'/C)dQ' = Q²/2C = ½CV²
E = Q²/(2C)	Q and C known	Direct integration of work done
E = ½QV	Q and V known	Substitute Q=CV into ½CV²

Table B — RC Time Constant τ = RC Key Values

Time	Discharge V/V₀	Charge V/V_s	% Discharged	Note
t = 0	100%	0%	0%	Initial state
t = τ	36.79%	63.21%	63.21%	1/e = 0.3679
t = 2τ	13.53%	86.47%	86.47%	e⁻²
t = 3τ	4.98%	95.02%	95.02%	e⁻³
t = 4τ	1.83%	98.17%	98.17%	e⁻⁴
t = 5τ	0.67%	99.33%	99.33%	Practical full discharge

Table C — Common Dielectric Constants (εᵣ)

Material	εᵣ	Notes
Vacuum / Air	1.000	Reference value
Teflon (PTFE)	2.1	Low-loss RF capacitors
Polyethylene	2.25	Cable insulation
Paper	3.5	Old capacitors
Mica	6.0	Precision capacitors
Glass	7.0	—
Alumina (Al₂O₃)	9.8	Ceramic capacitors
Water	80	Poor insulator, reference
Barium titanate	1200	High-C ceramic capacitors

Table D — Capacitance Prefixes Quick Reference

Prefix	Symbol	Value (F)	Common Use
Farad	F	1	Supercapacitors
millifarad	mF	10⁻³	Large electrolytic
microfarad	μF	10⁻⁶	Most common!
nanofarad	nF	10⁻⁹	Signal circuits
picofarad	pF	10⁻¹²	RF / high frequency

Energy Stored in a Capacitor — Three Equivalent Formulas

The energy stored in a capacitor can be calculated using any of three mathematically equivalent expressions. Each uses a different pair of the four fundamental quantities (C, V, Q, E). The most important energy stored in capacitor formula is:

E = ½CV² E = Q²/(2C) = ½QV — all three are identical

All three capacitor energy equations are derived from the fundamental definition: the energy stored in a capacitor equals the work done moving charge against the increasing voltage. As charge accumulates on the plate, the voltage rises linearly (V=Q/C), so:

E = ∫₀Q (Q'/C) dQ' = [Q'²/2C]₀Q = Q²/2C = ½CV² (substituting Q=CV). This derivation is why the capacitor energy stored formula has a ½ — the voltage starts at zero and rises to V, so the average voltage during charging is V/2.

Formula	Variables	Example (C=100μF, V=12V)
E = ½CV²	C and V known	½×10⁻⁴×144 = 7.2×10⁻³ J
E = Q²/(2C)	Q and C known	(1.2×10⁻³)²/(2×10⁻⁴) = 7.2×10⁻³ J
E = ½QV	Q and V known	½×1.2×10⁻³×12 = 7.2×10⁻³ J

The energy of a capacitor formula E=½CV² is the most-used form because capacitance C and supply voltage V are the most commonly specified parameters. The formula for energy stored in a capacitor in all three forms gives exactly 7.2 mJ for a 100μF capacitor charged to 12V. This capacitor stored energy formula applies to all capacitor types — electrolytic, ceramic, film, and supercapacitor.

Capacitor Charge Formula — Q = CV

The fundamental capacitor charge formula Q = CV defines the relationship between charge Q (Coulombs), capacitance C (Farads), and voltage V (Volts). Rearranging gives three forms:

Q = C × V — charge stored (Coulombs)
V = Q / C — voltage from charge and capacitance
C = Q / V — capacitance from charge and voltage

The unit definition: 1 Farad = 1 Coulomb/Volt. A 1 Farad capacitor stores 1 Coulomb at 1 Volt. Why are real capacitors in μF, nF, pF? One Farad is an enormous capacitance — a parallel plate capacitor with 1mm air gap would need ~9×10¹² m² of plate area to achieve 1 Farad. In practice, most capacitors range from picofarads (pF = 10⁻¹² F) for RF circuits up to thousands of microfarads for power supplies.

How to Calculate Energy Stored in a Capacitor — Step-by-Step

To calculate energy stored in a capacitor, follow this four-step method:

Convert capacitance to Farads: 100μF = 100×10⁻⁶ F = 1×10⁻⁴ F (never skip this step!)
Identify voltage: ensure V is in Volts
Apply E=½CV²: E = 0.5 × C_in_Farads × V²
Convert to preferred units: 7.2×10⁻³ J = 7.2 mJ = 7200 μJ = 0.002 Wh

Example 1 — Camera Flash Capacitor: C=100μF, V=300V

C = 100×10⁻⁶ F = 1×10⁻⁴ F
E = ½ × 1×10⁻⁴ × (300)² = ½ × 1×10⁻⁴ × 90000
E = 4.5 J | Q = 1×10⁻⁴ × 300 = 30 mC

Example 2 — Cardiac Defibrillator: C=150μF, V=2000V

C = 150×10⁻⁶ F
E = ½ × 150×10⁻⁶ × (2000)² = ½ × 150×10⁻⁶ × 4×10⁶
E = 300 J — delivered in milliseconds to restart the heart

Example 3 — Supercapacitor: C=1F, V=2.7V

E = ½ × 1 × (2.7)² = ½ × 7.29
E = 3.645 J | Q = 1 × 2.7 = 2.7 C

RC Circuit — Charging and Discharging

The time constant τ = RC governs how quickly a capacitor charges or discharges through a resistor. It is the fundamental parameter of any RC circuit — the time for voltage to fall to 36.8% (1/e) during discharge, or rise to 63.2% of supply during charging.

V(t) = V₀ × e^(−t/τ) [discharge] | V(t) = Vs × (1 − e^(−t/τ)) [charge] τ = RC | After 5τ: 99.33% charged / 0.67% remaining (practical "fully charged/discharged")

Physical interpretation of τ: it is the time it would take to fully discharge at the initial rate (the tangent at t=0 crosses zero at exactly t=τ). After exactly one time constant, 63.2% of the energy has been delivered to the load. After five time constants (5τ), the capacitor is considered fully charged or discharged for all practical purposes.

RC Discharge Example: C=470μF, R=10kΩ, V₀=9V, find V at t=4.7s

τ = R × C = 10000 Ω × 470×10⁻⁶ F = 4.7 s
t/τ = 4.7/4.7 = 1.000 (exactly one time constant)
V(4.7) = 9 × e^(−1) = 9 × 0.36788 = 3.311 V
Q(4.7) = C×V = 470×10⁻⁶ × 3.311 = 1.556 mC
E_remaining = ½×470×10⁻⁶×(3.311)² = 2.575 mJ (86.5% dissipated)

Capacitors in Series and Parallel

Capacitors combine in the opposite way to resistors. Parallel capacitors add their capacitances (like resistors in series add resistances); series capacitors combine using reciprocals (like resistors in parallel).

Configuration	Formula	Result vs Individual
Parallel	C_total = C₁ + C₂ + ... + Cₙ	Greater than largest
Series	1/C_total = 1/C₁ + 1/C₂ + ... + 1/Cₙ	Less than smallest
Two in series	C_total = C₁C₂/(C₁+C₂)	Less than both

Physical reason: parallel capacitors effectively add plate area (more charge at same voltage → more capacitance). Series capacitors effectively increase the plate separation (less capacitance). In series, all capacitors carry the same charge Q; voltages add up. In parallel, all have the same voltage V; charges add up.

Series: C₁=10μF, C₂=22μF → C_total=?

1/C_total = 1/10 + 1/22 = 0.1 + 0.04545 = 0.14545
C_total = 1/0.14545 = 6.875 μF (less than 10μF, the smaller)

Parallel: C₁=10μF, C₂=22μF → C_total=?

C_total = 10 + 22 = 32 μF (greater than 22μF, the larger)

What Is Capacitance? — Physical Definition and Units

A capacitor stores energy stored in a capacitor in the electric field between two conducting plates separated by a dielectric insulator. Capacitance C = Q/V is defined as the charge stored per unit voltage. The energy stored in a capacitor using the parallel plate formula:

C = ε₀ × εᵣ × A / d ε₀ = 8.854×10⁻¹² F/m | εᵣ = dielectric constant | A = plate area | d = separation

Why dielectrics increase capacitance: the dielectric material polarizes in the electric field, partially canceling the field between the plates. This allows more charge to be stored at the same voltage — increasing capacitance by the factor εᵣ. Barium titanate (εᵣ≈1200) allows capacitors thousands of times smaller than air-gap designs.

Where is energy stored in a capacitor? In the electric field between the plates. The energy density is u = ½ε₀εᵣE² J/m³. This is analogous to magnetic energy stored in an inductor's magnetic field.

Capacitor Energy Applications — From Flash to Defibrillator

The energy stored in a capacitor finds application wherever rapid energy delivery is needed — capacitors provide high power density (fast discharge) though lower energy density than batteries.

1. Camera Flash: C=100μF, V=300V

E = ½CV² = ½×100×10⁻⁶×90000 = 4.5 J. τ with R=10Ω: τ = RC = 10×100×10⁻⁶ = 1ms. The flash fires in ~1ms — 4.5 J in 1ms = 4500 W peak power.

2. Cardiac Defibrillator: C=150μF, V=2000V

E = ½×150×10⁻⁶×(2000)² = 300 J. Delivered through the chest in ~10ms. The capacitor must be charged from a battery (takes ~5 seconds) then discharged almost instantaneously.

3. Car Audio Capacitor: C=1F, V=14V

E = ½×1×(14)² = 98 J. Acts as a local energy reservoir for the amplifier during bass peaks, preventing voltage sag.

4. Supercapacitor Bank: C=500F, V=2.7V

E = ½×500×(2.7)² = 1822.5 J = 0.506 Wh. Used for regenerative braking energy recovery in hybrid vehicles.

Common Mistakes in Capacitor Energy Calculations

Mistake 1 — Not converting μF to F (the most common error)

❌ Wrong: E = ½ × 100 × 12² = ½ × 100 × 144 = 7200 J
✅ Correct: E = ½ × (100×10⁻⁶) × 144 = 7.2×10⁻³ J = 7.2 mJ
Always convert: 100μF = 100×10⁻⁶ = 0.0001 F before using the energy stored in capacitor formula

Mistake 2 — Forgetting the ½ factor

❌ Wrong: E = CV² = 10⁻⁴ × 144 = 0.0144 J (twice the actual value)
✅ Correct: E = ½CV² = 0.5 × 10⁻⁴ × 144 = 7.2×10⁻³ J

Mistake 3 — Using E=QV instead of E=½QV

❌ Wrong: E = QV = 1.2×10⁻³ × 12 = 14.4×10⁻³ J
✅ Correct: E = ½QV = 0.5 × 1.2×10⁻³ × 12 = 7.2×10⁻³ J

Mistake 4 — Thinking τ is the time to fully discharge

❌ Wrong: "After τ = 4.7s the capacitor is fully discharged"
✅ Correct: After τ, 36.8% voltage REMAINS. After 5τ (23.5s), only 0.67% remains — that's the practical "fully discharged" threshold

Mistake 5 — Series capacitance gives MORE total capacitance

❌ Wrong: "Two 10μF in series give 20μF"
✅ Correct: Two 10μF in series give C_total = 10×10/(10+10) = 5μF — HALF of either one. Series capacitors give LESS capacitance than the smallest.

Worked Examples — 8 Complete Problems

1. C=100μF, V=12V → find Q, E

C = 1×10⁻⁴ F
Q = CV = 1×10⁻⁴ × 12 = 1.2×10⁻³ C = 1.2 mC
E = ½CV² = ½×1×10⁻⁴×144 = 7.2×10⁻³ J = 7.2 mJ

2. C=470μF, V=400V → find E

C = 470×10⁻⁶ F
E = ½ × 470×10⁻⁶ × (400)² = ½ × 470×10⁻⁶ × 160000
E = 37.6 J (defibrillator scale)

3. E=1J, V=100V → find C

E = ½CV² → C = 2E/V² = 2×1/(100)² = 2/10000
C = 2×10⁻⁴ F = 200 μF

4. Q=50μC, C=10μF → find V, E

V = Q/C = 50×10⁻⁶ / 10×10⁻⁶ = 5 V
E = ½QV = ½ × 50×10⁻⁶ × 5 = 125×10⁻⁶ J = 125 μJ

5. RC discharge: C=10μF, R=100kΩ, V₀=5V, find V at t=1s

τ = RC = 100000 × 10×10⁻⁶ = 1.0 s
V(1) = 5 × e^(−1/1) = 5 × 0.36788 = 1.839 V (36.8% of initial)

6. Series: C₁=10μF, C₂=22μF → C_total

1/C_total = 1/10 + 1/22 = 0.1 + 0.04545 = 0.14545
C_total = 6.875 μF

7. Parallel: C₁=10μF, C₂=22μF → C_total

C_total = 10 + 22 = 32 μF

8. Find τ for discharge from 9V to 1V: R=47kΩ, C=100μF

τ = RC = 47000 × 100×10⁻⁶ = 4.7 s
t = −τ × ln(V_target/V₀) = −4.7 × ln(1/9) = −4.7 × (−2.197)
t = 10.33 s = 2.20τ

Frequently Asked Questions — Capacitor Energy

What is the formula for energy stored in a capacitor?

The energy stored in a capacitor formula has three equivalent forms: E = ½CV² (most common), E = Q²/(2C), and E = ½QV. All give identical results. For C=100μF at V=12V: E = ½ × 100×10⁻⁶ × 144 = 7.2×10⁻³ J = 7.2 mJ. Always convert capacitance to Farads before using the capacitor energy stored formula.

How do you calculate capacitor charge?

Use Q = C × V. Example: C=100μF, V=12V → Q = 100×10⁻⁶ × 12 = 1.2×10⁻³ C = 1.2 mC. Rearranging: V = Q/C and C = Q/V. The unit of capacitance 1 Farad = 1 Coulomb/Volt confirms the relationship.

What is the time constant of an RC circuit?

The time constant τ = RC (in seconds when R is in Ohms and C in Farads) determines the speed of charge/discharge. After one τ: 63.2% charged (36.8% remains if discharging). After 5τ: 99.33% charged (0.67% remains) — considered fully done in practice. Example: R=10kΩ, C=470μF → τ = 10000 × 470×10⁻⁶ = 4.7 seconds.

What is the difference between series and parallel capacitors?

Parallel: C_total = C₁ + C₂ + ... (total is greater than largest — adds plate area). Series: 1/C_total = 1/C₁ + 1/C₂ + ... (total is less than smallest — like increasing plate separation). For C₁=10μF, C₂=22μF: parallel = 32μF; series = 6.875μF. This is opposite to resistors.

Where is energy stored in a capacitor?

Energy stored in a capacitor resides in the electric field between the two conducting plates. The energy density is u = ½ε₀εᵣE² J/m³, where E is the electric field strength (V/d). The total energy E = ½CV² equals this density integrated over the volume between the plates.

Why does the energy formula for a capacitor have a ½ factor?

As the capacitor charges from 0 to V, the voltage increases linearly (V=Q/C). The work done moving each incremental charge dQ is V×dQ, but V is increasing. The total energy = ∫₀Q (Q'/C)dQ' = Q²/2C = ½CV². The factor ½ arises because the average voltage during charging is V/2, not V. The other ½ of the supplied energy is dissipated as heat in the series resistance.

What is a Farad?

A Farad (F) is the SI unit of capacitance: 1 F = 1 C/V (one Coulomb per Volt). One Farad is an enormous capacitance — a parallel plate capacitor with 1mm air gap would need ~9×10¹² m² of plate area. Real capacitors range from picofarads (pF = 10⁻¹² F) for RF circuits to single-digit Farads for supercapacitors. Microfarads (μF = 10⁻⁶ F) are the most common unit in practice.

How long does it take a capacitor to fully discharge?

Theoretically never — the exponential V = V₀e^(−t/RC) asymptotically approaches zero. In practice, after 5τ = 5RC, the voltage is only 0.67% of V₀, considered fully discharged. For R=10kΩ, C=470μF: τ=4.7s, full discharge ≈ 5×4.7 = 23.5 seconds. To find time to reach any target voltage: t = −τ × ln(V_target/V₀).

Related Calculators

Quick Formulas

E = ½CV²Energy from C and V — most common

E = Q²/(2C)Energy from Q and C

E = ½QVEnergy from Q and V

Q = C × VCharge stored (Coulombs)

τ = R × CRC time constant

V(t) = V₀e^(-t/τ)Discharge voltage

V(t) = Vs(1-e^(-t/τ))Charging voltage

C_par = C₁+C₂+...Parallel capacitors

1/C_ser = Σ(1/Cᵢ)Series capacitors

C = ε₀εᵣA/dParallel plate capacitance

Quick Examples

🔊 Car audio: 100μF, 12V → 7.2mJ

🔋 Supercap: 1F, 2.7V → 3.6J

📷 Flash: E=1J, V=400V → C

⏱ RC τ=4.7s timing circuit

📷 Camera flash discharge

RC Time Constants

At t=τ:
36.8% remains (discharge)
63.2% charged (charge)

At t=3τ:
5.0% remains
95.0% charged

At t=5τ:
0.67% remains ← "fully done"
99.33% charged

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Shahid Ali is the creator and lead developer of SciSolveLab, a platform dedicated to making complex scientific and mathematical computations accessible. With a deep background in physics, thermodynamics, and wave mechanics, Shahid's work is driven by the belief that robust, accurate mathematical tools should be just a click away for students, engineers, and researchers.

Capacitor Charge Calculator — Energy, Charge, Voltage & RC Circuit

Capacitor Charge Calculator

Energy Stored in a Capacitor — Three Equivalent Formulas

Capacitor Charge Formula — Q = CV

How to Calculate Energy Stored in a Capacitor — Step-by-Step

Example 1 — Camera Flash Capacitor: C=100μF, V=300V

Example 2 — Cardiac Defibrillator: C=150μF, V=2000V

Example 3 — Supercapacitor: C=1F, V=2.7V

RC Circuit — Charging and Discharging

RC Discharge Example: C=470μF, R=10kΩ, V₀=9V, find V at t=4.7s

Capacitors in Series and Parallel

Series: C₁=10μF, C₂=22μF → C_total=?

Parallel: C₁=10μF, C₂=22μF → C_total=?

What Is Capacitance? — Physical Definition and Units

Capacitor Energy Applications — From Flash to Defibrillator

1. Camera Flash: C=100μF, V=300V

2. Cardiac Defibrillator: C=150μF, V=2000V

3. Car Audio Capacitor: C=1F, V=14V

4. Supercapacitor Bank: C=500F, V=2.7V

Common Mistakes in Capacitor Energy Calculations

Mistake 1 — Not converting μF to F (the most common error)

Mistake 2 — Forgetting the ½ factor

Mistake 3 — Using E=QV instead of E=½QV

Mistake 4 — Thinking τ is the time to fully discharge

Mistake 5 — Series capacitance gives MORE total capacitance

Worked Examples — 8 Complete Problems

1. C=100μF, V=12V → find Q, E

2. C=470μF, V=400V → find E

3. E=1J, V=100V → find C

4. Q=50μC, C=10μF → find V, E

5. RC discharge: C=10μF, R=100kΩ, V₀=5V, find V at t=1s

6. Series: C₁=10μF, C₂=22μF → C_total

7. Parallel: C₁=10μF, C₂=22μF → C_total

8. Find τ for discharge from 9V to 1V: R=47kΩ, C=100μF

Frequently Asked Questions — Capacitor Energy

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Capacitor Charge Calculator — Energy, Charge, Voltage & RC Circuit

Capacitor Charge Calculator

Energy Stored in a Capacitor — Three Equivalent Formulas

Capacitor Charge Formula — Q = CV

How to Calculate Energy Stored in a Capacitor — Step-by-Step

Example 1 — Camera Flash Capacitor: C=100μF, V=300V

Example 2 — Cardiac Defibrillator: C=150μF, V=2000V

Example 3 — Supercapacitor: C=1F, V=2.7V

RC Circuit — Charging and Discharging

RC Discharge Example: C=470μF, R=10kΩ, V₀=9V, find V at t=4.7s

Capacitors in Series and Parallel

Series: C₁=10μF, C₂=22μF → C_total=?

Parallel: C₁=10μF, C₂=22μF → C_total=?

What Is Capacitance? — Physical Definition and Units

Capacitor Energy Applications — From Flash to Defibrillator

1. Camera Flash: C=100μF, V=300V

2. Cardiac Defibrillator: C=150μF, V=2000V

3. Car Audio Capacitor: C=1F, V=14V

4. Supercapacitor Bank: C=500F, V=2.7V

Common Mistakes in Capacitor Energy Calculations

Mistake 1 — Not converting μF to F (the most common error)

Mistake 2 — Forgetting the ½ factor

Mistake 3 — Using E=QV instead of E=½QV

Mistake 4 — Thinking τ is the time to fully discharge

Mistake 5 — Series capacitance gives MORE total capacitance

Worked Examples — 8 Complete Problems

1. C=100μF, V=12V → find Q, E

2. C=470μF, V=400V → find E

3. E=1J, V=100V → find C

4. Q=50μC, C=10μF → find V, E

5. RC discharge: C=10μF, R=100kΩ, V₀=5V, find V at t=1s

6. Series: C₁=10μF, C₂=22μF → C_total

7. Parallel: C₁=10μF, C₂=22μF → C_total

8. Find τ for discharge from 9V to 1V: R=47kΩ, C=100μF

Frequently Asked Questions — Capacitor Energy

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