# What needs to happen?

Need to answer: Theory: What is it? How does it work? Practice: Homework problems Possible permutations

# Circuits 1 Outline

## Units and Scales

### International System of Units (SI)

def: seven basic units upon which all others are based

#### Units

Base Quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin k
amount of substance mole mol
luminous intensity candela cd

#### Prefixes

Factor Name Symbol
femto f 10^-15
pico p 10^-12
nano n 10^-9
micro μ 10^-6
milli m 10^-3
centi c 10^-2
kilo k 10^3
mega M 10^6
giga G 10^9
tera T 10^12

## Charge, Current, Voltage, Power

### TODO: Nomenclature Disambiguation

• Describe the difference between unit, dimension, and symbol in terms of dimensional analysis.

### Charge

def: A physical property of matter that causes it to experience a force when placed in an electromagnetic field.

unit: Coulombs dimension: C symbol: Q or q

One Coulomb is the magnitude of charge of $6.242*10^18 * electrons or protons. $$1C = 1A*s = 1F*V$$ ### Current def: The flow of electrical charge (understood as the movement of electrons). unit: Ampere dimension: A symbol: I or i $$1A = 1C / s$$ (as above) NOTE: *amp-hours* is another way to write the amount of charge a battery has. Just do a little algebra and see.  ### Voltage def: the electric potential energy between two points per unit electric charge. unit: Volt dimension: V symbol: V or v $$V = \frac{ N * M}{C} = \frac{ kg * m^2 }{ A *s^3 }$$ ### Power def: Literally power is change in energy over change in time, in this instance it is the rate at which electrical energy is transferred by a circuit. unit: Watts dimension: W symbol: P $$P = V * I = \frac{V^2}{R} = I^2 * R$$ Peak Power: the rate of energy flow a) at its peak, or b) over the time of discharge (ex, a PWM signal). ## TODO: Resistance ## Passive Sign Convention def: an arbitrary and universally accepted method of labeling potential and current in an electrical circuit. ### Reference Directions For Current, Voltage, and Power The reference directions are given for a passive device that is assumed to be ‘consuming’ or ‘dissipating’ power. In this instance$p=v*i$and$r=v/i$. For those signs, current flows from the positive terminal of the device to the negative terminal and potential is higher on the positive side. For a device that is a load charge moves through an e-field gradient from a higher energy state, positive, to a lower energy state, negative. For a device that is a ‘source’ the charge is forced in the opposite direction, against the e-field gradient. The signs in this case are opposite:$p=-v*i$and$r=-v/i\$.

Source Power Resistance
load p > 0 r > 0
source p < 0 r < 0

## Ohm’s Law

$$V = I * R$$

## Sources, Nodes, Paths, Loops, and Branches

### Sources

These sources are considered “ideal” and are labeled as such. More realistic representations will follow.

### Branches

def: any single element withing a circuit

• add some examples from homeworks…

### Nodes

def: Nodes connect branches (elements) together.

• add some examples from homeworks…

### Paths

def: any combination of elements, nodes, and branches

• add some examples from homeworks…

### Loops

def: any closed path in a circuit

• add some examples from homeworks…

## Capacitors

• symbol
• current > voltage relationship
• integral voltage > current relationship
• energy storage
• in series and parallel
• characteristics of an ideal capacitor

## Inductors

• symbol
• voltage > current relationship
• integral current-voltage relationship
• energy storage
• in series and parallel
• characteristics of an ideal inductor