# Definitions and Basic Concepts.
## Introduction
- Basic field and circuit concepts
## Electric Charge and Coulomb's Law
[[Coulomb's Law]]
## [[Electric Current]]asdfjkl;asdfjkiol;asdfjiko
- Symbol $I$
- unit of *amperes* ($A$)
### Direct Current (DC)
- unidirectional transfer of electrons through a conductor
## [[Voltage]]
- Symbol $V$
- unit of *volts* ($V$)
## [[Power and Energy]]
### Energy
$
U = QV\quad(\text{J})
$
### Power
$
P = \frac{dU}{dt}=V\frac{dQ}{dt}=VI\quad(\text{W})
$
## Units, Dimensions, and Constants
| Quantity | Symbol | Dimensions | SI Unit |
| ------------------------ | ---------- | ------------------------------------------------------------------------------------------------------ | ----------------------------------------- |
| Electric charge | $Q$ | $\left[\text{A}\right]\left[\text{T}\right]$ | coulomb, $\text{C}$ |
| Electric potential | $V$ | $\left[\text{M}\right]\left[\text{A}\right]^{-1}\left[\text{L}\right]^2\left[\text{T}\right]^{-3}$ | volt, $\text{V}$ |
| Current | $I$ | $\left[\text{A}\right]$ | ampere, $\text{A}$ |
| Electric field intensity | $E$ | $\left[\text{M}\right]\left[\text{A}\right]^{-1}\left[\text{L}\right]\left[\text{T}\right]^{-3}$ | volt/meter, $\text{V/m}$ |
| Electric flux density | $D$ | $\left[\text{A}\right]\left[\text{L}\right]^{-2}\left[\text{T}\right]$ | coulomb/meter<sup>2</sup>, $\text{V/m}^2$ |
| Permittivity | $\epsilon$ | $\left[\text{M}\right]^{-1}\left[\text{A}\right]^2\left[\text{L}\right]^{-3}\left[\text{T}\right]^4$ | farad/meter, $\text{F/m}$ |
| Resistance | $R$ | $\left[\text{M}\right]\left[\text{A}\right]^{-2}]\left[\text{L}\right]^2\left[\text{T}^{-3}\right]$ | ohm, $\mathrm{\Omega}$ |
| Capacitance | $C$ | $\left[\text{M}\right]^{-1}\left[\text{A}\right]^{2}\left[\text{L}\right]^{-2}\left[\text{T}\right]^4$ | farad, $\text{F}$ |
| Conductivity | $\sigma$ | $\left[\text{M}\right]^{-1}\left[\text{A}\right]^{2}\left[\text{L}\right]^{-3}\left[\text{T}\right]^3$ | siemens/meter, $\text{S/m}$ |
## Solved Problems
### 1.1
Two point charges of 50 $\mu\text{C}$ are held 1.5 $\text{m}$ apart in free space. What is the force of repulsion between the two charges?
> Using Coulomb's law:
> $
> F=k\frac{Q_1Q_2}{r^2}=\boxed{9\times10^9\left(\frac{\left(50\times10^{-6}\right)^2}{1.5^2}\right)=10\text{ N}}
> $
### 1.2
Find the electric field intensity 1.5 $\text{m}$ from a 50 $\mu\text{C}$ charge in free space
> Definition of electric field intensity:
> $
> E=\lim_{Q_2\to0}\frac{F}{Q_2}
> $
> Substitute into Coulomb's law:
> $
> E=k\frac{Q_1}{r^2}=\boxed{9\times10^9\left(\frac{50\times10^{-6}}{1.5^2}\right)=200\text{ kN/C}=200\text{ kV/m}}
> $
### 1.3
Two point charges $Q_1=50\mu\text{C}$, and $Q_2=25\mu\text{C}$ are separated by a distance of 1 $\text{m}$ in air. At what distance from $Q_1$ will the electric field intensity be zero?
# Circuit Elements and Laws
## Circuit Notions
Elements:
- Resistance
- Capacitance
- Inductance
- Voltage source
- Current source
Terminology:
- circuit/network
- interconnection of circuit elements
- node
- junction of two or more elements
## Element Voltage-Current Relationships
Resistors
> $v=Ri\qquad i=Gv$
> $G=\frac{1}{R} \quad\left[\text{Siemens (S)}\right]\quad \text{conductance}$
Capacitors
> $C=\frac{Q}{V}=\frac{q}{v}$
*Q* - steady state charge
*V* - steady state voltage
*q* - transient charge
*q* - transient voltage
$i=\frac{dq}{dt}$
$v=\frac{1}{C}\int i\,dt\qquad\text{or}\qquad i=C\frac{dv}{dt}$
Inductors
> $v=L\frac{di}{dt}\qquad\text{or}\qquad i=\frac{1}{L}\int v\,dt$
## Series and Parallel Circuits
Resistance:
> $R_\text{series}=\sum_{k=1}^{n}R_k\qquad R_\text{parallel}=\sum_{k=1}^{n}\left(\frac{1}{R_k}\right)^{-1}$
### [[Voltage Division]]
### [[Current Division]]