# EC Mid (4/18)

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## Ch.1
### Engineering Notation
- $m \times 10^n,\ (n \mid 3)$

### Important Electrical Units
| Quantity | Q. Symbol | Unit | U. Symbol |
| ----------- | --------- | ------- | -------------- |
| Current | $I$ | Ampere | $A$ |
| Charge | $Q$ | Coulomb | $C$ |
| Voltage | $V$ | Volt | $V$ |
| Resistance | $R$ | Ohm | $\Omega$ |
| Conductance | $G$ | 1 / Ohm | $1\ /\ \Omega$ |
| Energy | $W$ | Joule | $J$ |
| Power | $P$ | Watt | $W$ |
| Capacity | $C$ | Farad | $F$ |

### Engineering Metric Prefix
| Symbol | Prefix | Number |
| ------ | ------ | ---------- |
| P | Pete | $10^{15}$ |
| T | Tera | $10^{12}$ |
| G | Giga | $10^9$ |
| M | Mega | $10^6$ |
| k | Kilo | $10^3$ |
| m | Milli | $10^{-3}$ |
| $\mu$ | Micro | $10^{-6}$ |
| n | Nano | $10^{-9}$ |
| p | Pico | $10^{-12}$ |
| f | Femto | $10^{-15}$ |

### Accuracy v.s. Precision
- Accuracy: the range of error
- Precision: repeatability

### Round-to-even
- $$a.\underline{b}c \left\{ \begin{array}{l} c > 5,\ b\ += 1 \\ c < 5,\ b\ += 0 \\ c = 5,\ \left\{ \begin{array}{l} (b + 1) \mid 2,\ b\ += 1 \\ b \mid 2,\ b\ += 0 \end{array} \right. \end{array} \right.$$

## Ch.2
- $$V = \frac{W}{Q},\ 1\ V = \frac{1\ J}{1\ C}$$
- $$I = \frac{Q}{t},\ 1\ A = \frac{1\ C}{1\ s}$$
- $$G = \frac{1}{R}$$
- $$1\ \Omega = \frac{1\ V}{1\ A}$$
- $$R = \frac{\rho l}{A}$$
- $l$: Length, $A$: Area
- A basic circuit: a voltage source, a path, a load

## Ch.3
- $$I = \frac{V}{R}\ (\text{Ohm's Law})$$
- $$P = \frac{W}{t},\ 1\ W = \frac{1\ J}{1\ s}$$
- $$1\ kWh = 3.6 \times 10^6\ J$$
- $$P = I^2 R,\ P = VI,\ P = \frac{V^2}{R}\ (\text{Watt's Law})$$
- $$1\ Ah = 3.6 \times 10^3\ C$$

## Ch.4
- A series circuit is one that has only one current path.
- Kirchhoff's Voltage Law (KVL):
- The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path.
- Voltage Divider Rule:
- The voltage drop across any give resistor in a series circuit is equal to the ratio of that resistor to the total resistance, multiplied by some voltage.

## Ch.5
- A parallel circuit is identified by the fact that it has more than one current path (branch) connected to a common voltage source.
- Parallel Circuit Rule for Resistance:
- The total resistance of resistors in parallel is the reciprocal of the sum of the reciprocals o;f the individual resistors.
- Kirchhoff's Current Law (KCL):
- The sum of the currents entering a node is equal to the sum of the currents leaving the node.
- Current Divider Rule:
- When current enters a node (junction) it divides into currents with values that are inversely proportional to the resistance values.

## Ch.6
- Loaded Voltage Divider Rule:
- ==TODO==
- Wheatstone Bridge:
- The Wheatstone bridge consists of a DC voltage source and four resistive arms forming two voltage dividers.
- The output is taken between the dividers.
- Frequently, one of the bridge resistors is adjustable.
- When the bridge is balanced, the output voltage is zero, and the products of resistances in the opposite diagonal arms are equal
- Thevenin's Theorem:
- Any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals.
- $V_{TH}$: The open circuit voltage between the two output terminals of a circuit.
- $R_{TH}$: The total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.
- The load resistor has no affect on the Thevenin parameters.
- GROUND!!!
- Maximum Power Transfer:
- ==TODO==
- Super Position Theorem:
- A way to determine currents and voltages in a linear circuit that has multiple sources by taking one source at a time and algebraically summing results.

## Ch.8
- Sine Wave:
- $A$: Amplitude
- $T$: Period
- $f$: Frequency
- $$f = \frac{1}{T},\ T = \frac{1}{f}$$
- AC Generator (Alternator)
- Alternating Current (AC) / Alternative Voltage:
- $V_P$: Amplitude
- $$V_{PP} = 2 \times V_P$$
- $$V_{rms} = \frac{1}{\sqrt{2}} \times V_P \approx 0.707 \times V_P$$
- $$V_{avg} = 0$$
- (Half-Cycle Average)
$$V_{h.c.avg} = \frac{2}{\pi} \times V_P \approx 0.637 \times V_P$$
- $V_P$: Peak voltage, $\theta$: Angle in rad or degrees, $\phi$: Phase shift
- $$v = V_P \sin{\theta},\ v = V_P \sin{(\theta \pm \phi)}$$
- $$P = I_{rms}^2 R,\ P = V_{rms} I_{rms},\ P = \frac{V_{rms}^2}{R}$$
- If the voltage would never go across 0 voltage, then this is a DC (directive current)
- Square Wave
- Triangular Wave
- Sawtooth Wave
- Harmonics

## Ch.9
- Capacitor:
- $C$: Capacity is the ratio of charge to voltage
- $$C = \frac{Q}{V},\ 1\ F = \frac{1\ C}{1\ V}$$
- $$C = \epsilon_0 \frac{A}{d}$$
- $$W = \frac{1}{2} C V^2$$
- Series Capacitors:
- $$C_T = \frac{1}{\frac{1}{C_1} + ... + \frac{1}{C_n}}$$
- All capacitors of a series capacitors store the same amount of charge
- Parallel Capacitors:
- $$C_T = C_1 + ... + C_n$$