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: $R_{eq}={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}$

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

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 ${\frac {F_{m}}{L}}=2k_{\rm {A}}{\frac {I_{1}I_{2}}{r}}$