**Capacitor: **two conducting plates charged with equal amount of charge of opposite signs, with insulator in between (we assume a vacuum unless said otherwise)

Three quantities characterize a capacitor: **1) **surface charge density **2) **capacitance **3) **dielectric constant

**Capacitance **(q= C x ∆V) Unit**: **Farad (F)

*The potential difference across a parallel plate capacitor is proportional to the charge on the plates. The proportionality factor is called capacitance*

**Capacitance** is the ability of a body to hold an electrical charge. Capacitance is also a measure of the amount of electrical energy stored (or separated) for a given electric potential. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.* The ratio of charge on each plate to the potential difference arose the capacitor! *

**Large **capacitance **Small: **potential difference

**C= **(e0 xA)/ b

*The capacitance of parallel plate capacitor depends only on geometric properties; it is proportional to the area of the plates and inversely proportional to the width of the gap between the plates. *

**Dielectric constant (**k**)= **material constant (NO UNITS) [k x e0] represents the **permittivity of the dielectric! **

**C= **(e0 xA)**xk**/ b ß correction factor when outside of a vacuum as the insulator

Q= C x ∆V

**Case 1: **fixed charge (you disconnect the battery) so if capacitance **increases **potential different (voltage) **decreases **and vice versa

**Case 2: **flexible charge (still connected to battery and **potential difference remains constant**) so if you **increase **capacitance, you also increase **charge **to keep potential constant

*****Charge capacitors store electric potential energy! **

When you first transfer charge, ∆q, from one plate to the other, **NO WORK IS DONE because the capacitor still has 0 potential difference. **However as you continue to transfer the same amount of charge step by step, work is **required! **

Moving charges against the electrical force W= ∆q x ∆V

Overall process: W= (1/2)xQx∆Vfinal

**Electrical Current (Amperes= C/s) **

*An electric current is defined as the amount of charge transferred through a cross-sectional area of a conductor per time unit *

I= ∆q/ ∆t= n x e x vd x A

A force is required to move an electron along a wire (which is equal to F=ma, leading to small electron speed) ****electrons move in a direction opposite to the current. **

**Drift Velocity: **the motion of point charges is indicated

**Current is proportional to:** density of mobile point charges, drift velocity, geometric cross-sectional area of wire.

Due to its dependency on the cross-sectional area (**A**) the current **I **is not a parameter characteristic for the conductor material (**NOT A MATERIAL CONSTANT**)

**Current density (a/m^2): **J= I/A= n x e x vd

**Resistance**

Resistance against the flow of point charges through a conductor (relates potential difference to current) potential difference along a given conductor vs. current it carries! Increases with length, decreases with increase in A, cross-sectional area.

**R**= V/I = (p x l)/A (**units: **V/A=Ω)

**Resistivity: **proportionality factor between the magnitude of the electric field, which causes point charges to move, and current density which represents the charge flow rate. (**Material dependent)**

|E|= p x J (p=resistivity) (**units: **V x m/A)

**Materials behave Ohmically: **electrical field if proportional to current density

**Superconductors**: no resistivity at low temperatures

**Conductivity (****ϒ) **

Conductivity is defined as the inverse value of the resistivity: ( ϒ= 1/p) **units: **1/(Ωxm)

**Used the describe movement through a resistors than hindrance of motion of point charges.