Long Exam 2 Concepts (Capacitors)

Capacitor

A device consisting of two conductors separated by an insulator that stores electric potential energy and electric charge.

Capacitance (C)

The ratio of the magnitude of charge (Q) on one conductor to the potential difference (V) between them.

Farad (F)

The SI unit of capacitance; 1 F = 1 Coulomb per Volt (C/V).

Note: 1 F is very large; most problems use (μF, 10^-6).

Dielectric

A nonconducting material (insulator) like paper, plastic, or glass placed between capacitor plates.

Dielectric Constant (K)

A dimensionless number that represents how much a material increases the capacitance.

K = 1

How much K (Dielectric Constant) does a vacuum have?

Dielectric Breakdown

The failure of an insulator at very high voltages, resulting in a spark or short circuit.

Permittivity (ϵ)

A measure of how much a material "permits" an electric field.

ϵ = κϵ₀​

Formula

Permittivity if a Dielectric

Formula

Fundamental Capacitance

A = Area of plates (m²)

d = separation distance (m)

Formula

Capacitance (Parallel Plate)

K = Dielectric Constant

C₀ = Original Capacitance

Formula

Capacitance with Dielectric

Formula

Potential Energy Stored

Formula

Energy Density

Formula

Voltage/Field Relation

Formula

Surface Charge Density

Formula

Induced Charge Density

Increases

Increasing vs. Decreasing

If you increase the area (A): Capacitance (C) …

Decreases

Increasing vs. Decreasing

If you increase the distance (d): Capacitance (C) …

Charge (Q)

If you insert a Dielectric and the battery is disconnected, which one is constant Charge (Q) or Voltage (V)?

Voltage (V)

If you insert a Dielectric and the battery is connected, which one is constant Charge (Q) or Voltage (V)?

Capacitance (C): Increases by factor K

Voltage (V): Decreases

Electric Field (E): Decreases

Energy (U): Decreases

If we insert a Dielectric when the battery is disconnected, what will happen to the Capacitance (C), Voltage (V), Electric field (E), and Energy (U)?

Capacitance (C): Increases by factor K

Voltage (V): Constant

Electric Field (E): Increases

Energy (U): Increases

If we insert a Dielectric when the battery is connected, what will happen to the Capacitance (C), Voltage (V), Electric field (E), and Energy (U)?

Rule: Every capacitor has the same Charge (Q).

Formula

How to get the C_eq in a Series.

Rule: Every capacitor has the same voltage (V).

Formula

How to get the C_eq in a Parallel.