Labo Élec
electrical lab simulator
Reminder sheet
A capacitor stores charges and therefore energy; it charges and discharges with a time constant τ = R·C. Remember 63 % at τ and "done" at 5τ.
A capacitor is made of two conducting plates separated by an insulator. At a voltage U it stores a charge Q = C·U; C is its capacitance, in farads (in practice µF, nF, pF). It stores the energy W = ½ C U².
In parallel capacitances add up; in series their inverses add up. Charged through a resistor, it reaches 63 % of its final voltage after τ = R·C and ≈ 100 % after 5τ; in steady DC it passes no current.
| Quantity | Symbol | Unit |
|---|---|---|
| Charge | Q | C |
| Capacitance | C | F |
| Voltage | U | V |
| Quantity | Symbol | Unit |
|---|---|---|
| Energy | W | J |
| Quantity | Symbol | Unit |
|---|---|---|
| Equivalent capacitance | Céq | F |
| Quantity | Symbol | Unit |
|---|---|---|
| Time constant | τ | s |
| Resistance | R | Ω |
| Capacitance | C | F |
3-digit marking: two digits then number of zeros, in pF (104 = 100 000 pF = 100 nF).
A 100 µF capacitor is charged at 12 V. What charge and energy does it store? It is charged through R = 10 kΩ: time constant and charging time? Two such capacitors in series: equivalent capacitance?
Q = C · U = 100 × 10⁻⁶ × 12 = 1.2 × 10⁻³ C = 1.2 mC.
W = ½ · C · U² = 0.5 × 100 × 10⁻⁶ × 144 = 7.2 mJ.
τ = R · C = 10⁴ × 10⁻⁴ = 1 s: 63 % of 12 V (7.6 V) after 1 s, full charge (99 %) after 5τ = 5 s.
In series: 1/Ceq = 1/100 + 1/100, Ceq = 50 µF.
Capacitor charging through R: 63 % of the final voltage after τ = RC.