Capacitors
Introduced| English |
|---|
| capacitor/kəˈpæsɪtə/ |
| farad/ˈfæræd/ |
A camera flash: store charge slowly, dump it all at once
- A camera charges up quietly, then fires a burst of light in an instant.
- Behind it is a capacitor 电容器 — a device that stores electric charge and releases it fast.
- It is two conductors holding opposite charge, with a field trapped between them.
- Capacitors run flashes, smooth power supplies, and time circuits.
What a capacitor is
- A capacitor is two conducting plates separated by a small gap.
- Connect it to a voltage and one plate gains + charge, the other −.
- The capacitance $C = \dfrac{Q}{V}$ measures how much charge it stores per volt.
- Capacitance is measured in farads 法拉 ($1\ \text{F} = 1\ \tfrac{\text{C}}{\text{V}}$).
Charge up a capacitor
Watch charge build on the plates as the capacitor charges, then discharge.
A $2\ \text{F}$ capacitor is charged to $3\ \text{V}$. How much charge does it store, in $\text{C}$?
$Q = CV = 2 \times 3 = 6\ \text{C}$.
Capacitance is defined as:
$C = Q/V$ — charge stored per volt.
Capacitance is measured in ____.
$1\ \text{F} = 1\ \tfrac{\text{C}}{\text{V}}$.
Storing energy
- A charged capacitor stores energy $U = \tfrac12 C V^2$ in the field between its plates.
- Bigger capacitance or higher voltage means more stored energy.
- Unlike a battery, it can release its energy almost instantly — hence camera flashes.
- Charging and discharging take time, set by the circuit (next in RC circuits).
The same $2\ \text{F}$ capacitor at $3\ \text{V}$ stores how much energy, in $\text{J}$?
$U = \tfrac12 CV^2 = \tfrac12 (2)(9) = 9\ \text{J}$.
What sets the capacitance
- Bigger plates store more charge, so larger area ⇒ more capacitance.
- A smaller gap between plates ⇒ more capacitance (the charges attract more strongly).
- An insulating dielectric between the plates boosts capacitance further.
- So geometry, not voltage, decides a capacitor's capacitance.
A capacitor's capacitance changes when you raise the voltage across it.
Capacitance is fixed by geometry; raising $V$ stores more $Q$ but keeps $C = Q/V$ the same.
Select all changes that increase a capacitor's capacitance.
Bigger area, smaller gap and a dielectric all raise $C$. Voltage does not change $C$.
Capacitance $C = Q/V$ is a fixed property of the capacitor itself (its plates and gap) — it does not change when you change the voltage. Raising $V$ stores more charge $Q$, keeping the ratio $C$ the same.
A capacitor of $C = 2\ \text{F}$ is charged to $V = 3\ \text{V}$.
- Charge stored: $Q = CV = 2 \times 3 = 6\ \text{C}$.
- Energy stored: $U = \tfrac12 CV^2 = \tfrac12 (2)(3^2) = 9\ \text{J}$.
A capacitor stores charge on two plates; its capacitance $C = \dfrac{Q}{V}$ (in farads) is fixed by its geometry, not the voltage. It stores energy $U = \tfrac12 CV^2$ and can release it very fast — the basis of camera flashes and smoothing circuits.