Capacitance
A capacitor is a device that stores electric charge on two separated conductors, like a pair of metal plates. The more voltage you push across it, the more charge piles up — and capacitance tells you exactly how much charge you get for each volt. Bigger plates or a smaller gap between them let a capacitor hold more charge at the same voltage.
The formula
Q = C · V
- Q — charge (C): the amount of electric charge stored on the capacitor
- C — capacitance (F): how much charge the capacitor stores per volt applied
- V — voltage (V): the electrical push, or potential difference, across the capacitor
Worked example
A capacitor with a capacitance of 3 farads is connected across a 4 volt battery. How much charge does it store?
- C = 3 F
- V = 4 V
- Q = C · V
- Q = 3 F × 4 V
Q = 12 C
Test yourself
The same 3 farad capacitor is now connected to a 6 volt battery instead. How much charge does it store?
- 24 C
- 2 C
- Correct answer: 18 C
Right! Q = C × V, so 3 F × 6 V = 18 C.
For a parallel-plate capacitor, if you double the area of the plates but keep the gap the same, what happens to the capacitance?
- Correct answer: It doubles
- It stays the same
- It is cut in half
Exactly! C = ε₀A / d, so doubling the plate area A doubles the capacitance.
Where you see this
A smartphone touchscreen is a grid of tiny capacitors: your finger's presence changes the local capacitance, and the phone reads which spot changed. Computer memory chips are billions of microscopic capacitors, each holding charge for a logic bit — charged or not, one or zero.
Common mistakes
The core confusion is what capacitance is: C is a property of the device's geometry — plate area and gap, C = ε₀A / d — not something that grows because you charged it more. At fixed capacitance, charge simply tracks voltage, Q = C · V: a 3 F capacitor on a 6 V battery stores 18 C, twice what it stores on 3 V. And a bigger gap weakens a capacitor — the plates must be closer, not farther, to hold more at the same voltage.
How it connects
The voltage across a capacitor exists because charge is piled up against Coulomb's law — that stored push is what the previous lesson's force geometry produces in hardware. The circuits module already met this device: the RC time constant τ = R · C is how fast it fills. Next, currents reveal they do something else entirely: make magnetic fields.