Capacitor calculator (series, parallel, charge and energy)
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Result
| Capacitor | Capacitance | Voltage | Charge | Energy |
|---|---|---|---|---|
| C1 | 10 µF | 7.197 V | 71.97 µC | 259 µJ |
| C2 | 22 µF | 3.271 V | 71.97 µC | 117.7 µJ |
| C3 | 47 µF | 1.531 V | 71.97 µC | 55.11 µJ |
Combine capacitors in series or parallel, and find the charge and voltage of each one, or work out the charge Q = C·V and the stored energy E = ½·C·V² of a single capacitor. A third mode gives the capacitance of a parallel-plate capacitor from the plate area, the gap and the dielectric, and checks whether the field would break down the air in the gap.
Step-by-step solution
Series: add the reciprocals
Charge and energy
Key formulas
- Time constant
- τ = RC | τ = L/R
- Response
- x(t) = x(∞) + [x(0) − x(∞)]·e−t/τ
- Capacitor at DC
- open circuit; vC cannot jump
How to calculate capacitors in series and parallel
- Parallel: the capacitors share the same voltage, so their charges add up. The equivalent capacitance is the sum: C = C₁ + C₂ + C₃.
- Series: every capacitor carries the same charge. Add the reciprocals: 1/C = 1/C₁ + 1/C₂ + 1/C₃. The result is smaller than the smallest capacitor.
- With a voltage V across the combination, the total charge is Q = C·V and the stored energy is E = ½·C·V².
- In series each capacitor has the voltage Vᵢ = Q/Cᵢ, so the smallest capacitor gets the largest voltage. In parallel each charge is Qᵢ = Cᵢ·V.
- For a parallel-plate capacitor, C = ε₀·εr·A/d with ε₀ = 8.854 × 10⁻¹² F/m, the plate area A in m² and the gap d in m.
Questions and answers
Why are capacitors in series and resistors in series opposite?
Resistances in series add because the current flows through each one in turn. Capacitors in series act like one capacitor with a thicker dielectric, so the capacitance falls; it is the reciprocals that add. In parallel the plate areas effectively add, so the capacitances add.
How much energy does a capacitor store?
E = ½·C·V² = ½·Q·V = Q²/(2C). A 470 µF capacitor charged to 25 V stores ½ × 470 × 10⁻⁶ × 25² = 0.147 J. Large capacitors can stay charged after the power is off, so discharge them before touching the leads.
What is the relative permittivity εr?
It says how much a dielectric increases the capacitance compared with vacuum. Air is about 1.0006, PTFE about 2.1, glass about 5 to 10 and ceramic dielectrics from about 10 to several thousand.
What voltage rating should a capacitor have?
Higher than the largest voltage it will see, usually with a margin of 20% to 50%. In series the voltages are not shared equally unless the capacitors are equal, so check each capacitor with Vᵢ = Q/Cᵢ.
Practise it yourself
Practise RC & RL transients
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.