Capacitors

Resistors dissipate energy (turn it into heat). Capacitors store energy — and release it later, on demand.

A camera flash is the textbook example. The battery slowly trickles charge into a capacitor over a couple of seconds. Then, when you press the shutter, the capacitor dumps all that stored energy in less than a millisecond — producing a brilliant burst of light far brighter than the battery alone could deliver. Same total energy as the battery provided, just released at a much higher rate.

The same physics powers defibrillators (slow charge from a battery, sudden discharge through a patient’s chest), camera flashes, audio amplifiers (capacitors smooth out the power supply), and the timing circuits in nearly every electronic device.

What Is a Capacitor?

At its simplest, a capacitor is just two conducting plates separated by a small gap. When connected to a battery, positive charge piles up on one plate and negative charge on the other. The plates don’t touch, so charge can’t flow between them — it just builds up, creating an electric field across the gap.

Capacitance

Capacitance measures how much charge a capacitor stores per volt applied.

Parallel Plate Capacitor

The most common capacitor geometry on the MCAT is the parallel plate capacitor: two flat plates of area $A$ separated by distance $d$.

The MCAT loves “what happens when you change one variable” questions:

• Double the plate area → capacitance doubles ($C \propto A$).
• Double the plate separation → capacitance halves ($C \propto 1/d$).
• Insert a dielectric → capacitance increases by a factor $\kappa$ (covered in §6.10).

The Electric Field Between the Plates

The electric field between the plates of a parallel plate capacitor is uniform (constant everywhere) and given by:

$E = \dfrac{V}{d}$

So field strength grows when voltage grows or plate separation shrinks. This uniform field is exactly why parallel plate capacitors are the go-to setup for MCAT problems about charged particles flying through electric fields — the math is much simpler with a uniform field than with the messy fields around point charges.

Energy Stored in a Capacitor

A charged capacitor stores electrical potential energy in the electric field between its plates.

That $\tfrac{1}{2}$ factor isn’t arbitrary. The voltage builds gradually as the capacitor charges. The first bit of charge is easy to add (low voltage opposing it), but the last bit has to push against the high voltage that’s already built up. Average voltage during the charging process is half the final voltage — hence the $\tfrac{1}{2}$.