Electrical Engineering/Quick Reference

Basics

Voltage: (V or v - Volts) The electrical potential between two points in a circuit.
Current: (I or i - Amperes) The amount of charge flowing through a part of a circuit.
Power: (W - Watts) Simply P = IV. It is the current times the voltage.
Source: A voltage or current source is the supplier for the circuit.
Resistor: (R measured in Ω - Ohms) A circuit element that "constricts" current flow.

Ohms law $V = I R$ or equivalently $I = \frac{V}{R}$ or $R = \frac{V}{I}$

Voltage Divider $V_{1} = \frac{R_{1}}{R_{1} + R_{2}} * V_{s}$

Resistors in Parallel $R_{e q} = \frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + . . . + \frac{1}{R_{n}}}$

and for the special case of two resistors in parallel: $R_{e q} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

Kirchhoff’s Voltage law: The algebraic sum of the voltages around a closed circuit path must be zero.

Kirchhoff’s Current Law: The sum of the currents entering a particular point must be zero.

Capacitors in an AC circuit: $I = C \frac{d V}{d t} = - ω C V_{0} \sin (ω t)$

In parallel: $C_{e q} = \sum_{i} C_{i} = C_{1} + C_{2} + \dots + C_{n}$

In series $\frac{1}{C_{e q}} = \sum_{i} \frac{1}{C_{i}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \dots + \frac{1}{C_{n}}$

Inductors in an AC circuit: $v (t) = L \frac{d i (t)}{d t}$

In parallel: $\frac{1}{L_{e q}} = \frac{1}{L_{1}} + \frac{1}{L_{2}} + \dots + \frac{1}{L_{n}}$

In series: $L_{e q} = L_{1} + L_{2} + \dots + L_{n}$

Special case: Two straight parallel wires $\frac{F_{m}}{L} = 2 k_{A} \frac{I_{1} I_{2}}{r}$