Physics
Capacitor calculator: capacitance, charge and energy
Clear the quantity you need and the formula rearranges. Plus the parallel-plate capacitor from its geometry, and the two wiring rules with the read-out for each component.
Why capacitors combine the opposite way to resistors
A capacitor does not store net charge: it stores separated charge. One plate takes +Q, the other −Q, and the total stays zero. What it holds is energy in the electric field between the plates, which is why it empties in an instant while a battery takes hours: the field collapses as soon as there is a path for the current.
The capacitance depends only on the geometry and the material, not on the charge or the voltage. Bigger plates hold more charge at the same voltage; closer plates make a stronger field for the same charge, hence a lower voltage, hence a larger capacitance. The dielectric multiplies the capacitance by its relative permittivity — about 1 in air, 2.2 in polypropylene, several thousand in ceramics.
The wiring rule is the reverse of the resistor one, and the reason is worth knowing. Putting two capacitors in parallel is like widening the plates, so the capacitances add. Putting them in series is like moving the plates apart, so the capacitance drops and the reciprocals add. Remember that parallel adds areas and you will never get the direction wrong again.
Common mistakes
- Applying the resistor rule to capacitors: in parallel the capacitances add, in series the reciprocals add. It is exactly the other way round.
- Forgetting that the energy goes as the square of the voltage: at half the voltage the energy is a quarter, not a half.
- Confusing the total charge with the charge on each component: in series the charge is the same on all of them, in parallel it is the voltage that is common. The table below shows which of the two divides up.
Frequently asked questions
How do you work out the equivalent capacitance in series?
Add the reciprocals and invert: 1/Ceq = 1/C₁ + 1/C₂ + … For just two capacitors there is the shortcut Ceq = (C₁·C₂)/(C₁+C₂). The result is always smaller than the smallest capacitance.
How much energy does a capacitor store?
U = ½·C·V². A 10 µF capacitor at 12 V stores 0.72 millijoules. The same energy can also be written ½·Q·V or Q²/(2C).
What determines the capacitance of a parallel-plate capacitor?
C = ε₀·εᵣ·A/d: it grows with the plate area and the permittivity, and falls with the separation. It depends on neither the charge nor the applied voltage.
What is the dielectric between the plates for?
Two things: it keeps the plates close without letting them touch, and it multiplies the capacitance by εᵣ, because its molecules polarise and reduce the field for the same charge. It does have a breakdown strength beyond which it fails.
How this calculation works
Definition: C = Q/V, with C in farads, Q in coulombs and V in volts. Parallel-plate capacitor: C = ε₀·εᵣ·A/d, with ε₀ = 8.854 × 10⁻¹² F/m. Energy stored: U = ½·C·V² = ½·Q·V = Q²/(2C). Field between the plates: E = V/d. Capacitors in parallel: Ceq = C₁ + C₂ + … + Cₙ; the voltage is common and each holds Qᵢ = Cᵢ·V. Capacitors in series: 1/Ceq = 1/C₁ + 1/C₂ + … + 1/Cₙ; the charge is common and each drops Vᵢ = Q/Cᵢ. For two in series: Ceq = (C₁·C₂)/(C₁ + C₂).
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