Electronics Equations and definitions

Quick reference for intro circuits. See Electronics Key concepts for meanings and Electronics Examples for use.

Core quantities

• Charge: $Q$, unit Coulomb ($\mathrm{C}$).
• Current: $I=\frac{dQ}{dt}$, unit Ampere ($\mathrm{A}=\mathrm{C}{\mathrm{s}}^{-1}$).
• Voltage: $V=\frac{W}{q}$, unit volt ($\mathrm{V}=\mathrm{J}{\mathrm{C}}^{-1}$).
• Resistance: $R=\frac{V}{I}$, unit ohm ($\Omega$).
• Power: $P=IV$, unit watt ($\mathrm{W}=\mathrm{J}{\mathrm{s}}^{-1}$).

Ohm’s law

For an ohmic Resistance:

$V=IR$

Equivalent power forms:

$P=IV=I^{2}R=\frac{V^2}{R}$

Kirchhoff rules

Junction rule, from charge conservation:

$\sum I_{in}=\sum I_{out}$

Loop rule, from energy conservation:

$\sum \Delta V=0$

Series and parallel resistors

Series: same current through each resistor.

$R_{eq}=R_1+R_2+\cdots$

Parallel: same voltage across each branch.

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$

Sign convention

Choose current directions and voltage polarities before writing equations. Negative answers usually mean the real direction/polarity is opposite your guess, not that the math failed.

Measurement reminders

An ideal voltmeter has very large resistance and is connected in parallel with the component being measured. An ideal ammeter has very small resistance and is connected in series. This matches the meanings of Voltage as a between-two-points quantity and Current as flow through a path.

Parent map: Electromagnetism MOC.