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 $$V = IR$$ or equivalently  $$I = \frac{V}{R}$$ or $$R = \frac{V}{I}$$

Resistors in series $$R = R1 + R2$$

Voltage Divider $$V_1 = \frac{R_1}{R_1 + R_2} * V_s$$

Resistors in Parallel $$R_{eq} = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}}$$

and for the special case of two resistors in parallel: $$R_{eq}=\frac{R_1R_2}{R_1 + R_2}$$

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
Capacitors in an AC circuit: $$ I = C \frac{dV}{dt} = -\omega {C}{V_\text{0}}\sin(\omega t)$$

In parallel: $$C_\mathrm{eq}= \sum_{i} C_i = C_1 + C_2 + \cdots + C_n$$

In series $$\frac{1}{C_\mathrm{eq}} = \sum_{i} \frac{1}{C_i} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}$$

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

In parallel: $$ \frac{1}{L_\mathrm{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots + \frac{1}{L_n}$$

In series: $$ L_\mathrm{eq} = L_1 + L_2 + \cdots + L_n \,\! $$

Ampere’s Force Law
Special case: Two straight parallel wires $$ \frac {F_m} {L} = 2 k_{\rm A} \frac {I_1 I_2 } {r}$$