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title: EC Mid (4/18)

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# 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:
    - $$C_T = C_1 + ... + C_n$$
