Capacitors and Dielectrics | MCAT Free Notes

Capacitors: Capacitance, Dielectrics, Energy Stored and Series vs Parallel

By StudyStore · Published 2026-11-05 · 2 min read · 427 words

A capacitor stores charge and energy in the electric field between two conductors. Capacitance C is how much charge it holds per volt. The MCAT checks three things: what C depends on, what happens when a dielectric is added, and that series and parallel rules are the reverse of resistors.

Core formulas

Quantity	Formula
Capacitance	C = Q / V
Parallel plate capacitance	C = ε₀A / d (times κ with a dielectric)
Energy stored	U = ½CV² = ½QV = Q²/2C
Field between plates	E = V / d
Parallel	C_eq = C₁ + C₂ + ...
Series	1/C_eq = 1/C₁ + 1/C₂ + ...

C grows with plate area A and shrinks as separation d grows. It depends only on geometry and the material between plates, not on Q or V.

Dielectrics

A dielectric is an insulator placed between the plates. It multiplies capacitance by its dielectric constant κ (greater than 1). What else changes depends on whether the battery is attached.

Condition	V	Q	E	C	U
Battery connected, dielectric added	Same	Rises by κ	Same	Rises by κ	Rises by κ
Battery disconnected, dielectric added	Falls by κ	Same	Falls by κ	Rises by κ	Falls by κ

Connected means V is fixed. Isolated means Q is fixed. Decide which is held constant before reasoning.

Series vs parallel

Capacitors in parallel share the same V and their charges add, so C adds. In series they share the same Q and their voltages add, so reciprocals add. Series always gives a C smaller than the smallest one.

Worked example

Two capacitors of 4 uF and 12 uF are placed in series across 12 V.

C_eq = 1/(1/4 + 1/12) = 1/(4/12) = 3 uF.
Total charge: Q = CV = 3 x 12 = 36 uC, the same on each capacitor.
Voltages: 36/4 = 9 V and 36/12 = 3 V, which add to 12 V.
Energy: ½(3 uF)(12 V)² = 216 uJ.

Common traps

Using resistor rules. For capacitors, parallel adds.
Thinking C depends on Q or V. It depends on A, d and κ.
Ignoring whether the battery is connected when a dielectric or the plate separation changes.
Forgetting the one-half in U.

One-minute recap

C = Q/V = κε₀A/d. U = ½CV². Parallel adds, series reciprocal. Dielectric raises C by κ. Battery on: V fixed. Battery off: Q fixed.

Check yourself: 5-question mini-quiz

Try each question first, then click it to reveal the answer.

1. The plate separation of an isolated, charged capacitor doubles. What happens to its capacitance?

It halves, because C is proportional to 1/d.

2. Two 6 uF capacitors are connected in series. What is the equivalent capacitance?

3 uF.

3. A dielectric is inserted while the battery stays connected. What stays the same?

The voltage across the plates, while charge and stored energy rise by the factor kappa.

4. What are the voltages across series capacitors of 4 uF and 12 uF with 12 V applied?

9 V across the 4 uF and 3 V across the 12 uF, since they hold equal charge.

5. How much energy does a 2 uF capacitor store at 10 V?

100 uJ, from one-half times 2 uF times 100 V squared.

Free MCAT sampler

Enter your email and download a real page set from a paid pack: the 3-page Amino Acids, Proteins and Enzymes cheat sheet (PDF). Confirm your email and short MCAT lessons follow. Free, no card.

Prefer not to sign up? The sampler is open to everyone: free notes, practice sets and the study schedule generator.

Written by StudyStore from standard scientific facts. Study aid only. Always check values against the reference your exam provides.