1. What Is Capacitance?
Think of a capacitor like an electrical water tank. The power supply is a pump
pushing water (charge) in. The "capacitance" is basically how wide the tank is — a wider tank
(bigger capacitance) can store more water (charge) for the same pump pressure (voltage).
Physically, a capacitor is just two metal plates facing each other, usually with an
insulating material called a dielectric sandwiched between them so charge can't jump
straight across. The circuit symbol is two parallel lines:
───┤ ├───
(two parallel lines = capacitor)
When you connect a capacitor to a battery, the battery doesn't push charge through the
capacitor (the dielectric blocks that) — instead it pushes electrons onto one plate
(making it negative) and pulls electrons off the other plate (making it positive).
The plates never touch, but they build up equal and opposite charge.
The Defining Equation
In plain English: capacitance is defined as the charge stored per unit potential
difference between the plates. The bigger the capacitance, the more charge you can
cram in for every volt you apply.
Watch out
1 Farad is a huge unit in practice — real capacitors are usually measured in
microfarads (μF, ×10⁻⁶), nanofarads (nF, ×10⁻⁹), or picofarads (pF, ×10⁻¹²). Always convert
to Farads before substituting into equations!
Common mixup
The letter "C" is used for two different things: the symbol for capacitance, AND
the unit of charge (Coulombs). Don't confuse "5 C of capacitance" with "5 C of charge" —
read the units carefully!
Practice Question 1
A parallel plate capacitor has a capacitance of 1 nF and is connected to
a voltage supply of 0.3 kV. Calculate the charge stored on the plates.
Practice Question 2
A capacitor stores 6 × 10⁻⁴ C of charge when the potential difference
across it is 12 V. Calculate its capacitance in μF.
2. Energy Stored by a Capacitor
Here's the subtle bit: charging a capacitor doesn't cost a constant amount of energy
per electron. At the start, the negative plate is nearly empty, so pushing on the first few
electrons is easy (little repulsion). But as more negative charge piles up, each new electron
you try to push on gets repelled harder by the ones already there. So the p.d. across the
capacitor rises as the charge builds up, and the work needed to add more charge increases too.
This is exactly why the relationship between charge and voltage is a straight line through
the origin (Q = CV), not a constant. And because work = charge × p.d., but p.d. is changing
the whole time, you can't just use W = QV directly — you need the average p.d. during
charging, which is why there's a factor of ½.
Area Under the Graph
If you plot potential difference V (y-axis) against charge Q (x-axis), you get a straight line
through the origin (since Q = CV, the gradient is 1/C). The energy stored is the area under
this line — which forms a right-angled triangle:
V (p.d.)
│ ● ← straight line, V ∝ Q
│ ╱ █
│ ╱ ████ Shaded area = energy stored
│ ╱ ██████ Area = ½ × base × height
│ ╱ ████████ = ½ × Q × V
│ ╱________________
0 Q (charge)
How to choose which formula
Given Q and V → use W = ½QV. Given C and V → use W = ½CV².
Given Q and C → use W = Q²/2C. They all come from substituting Q = CV into each other.
Practice Question 3
Calculate the change in energy stored in a capacitor of capacitance
1500 μF when the potential difference across it changes from 10 V to 30 V.
Practice Question 4
A 470 μF capacitor is charged to a p.d. of 9 V. How much energy is stored?