Electricity and Magnetism

Ohm's law and resistor networks

Ohm's law: $V=IR$, where $V$ is potential difference, $I$ is current, and $R$ is resistance. In series, the same current flows through every component and resistances simply add: $R_{total}=R_1+R_2+\dots$. In parallel, every branch has the same voltage across it and resistances combine as $\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\dots$

Electrical power and energy

Power delivered to a component: $P=VI=I^{2}R=\frac{V^2}{R}$. Energy transferred over time $t$: $E=Pt$.

Electrostatics

Like charges repel, unlike charges attract. Coulomb's law gives the force between two point charges: $F=\frac{k{Q}_1{Q}_2}{r^2}$, which decreases sharply as the distance $r$ increases. A charged rod can attract small, light, uncharged objects (like bits of paper) by inducing an opposite charge on the near side of the object -- this is induction, and doesn't require actual contact or charge transfer.

Magnetism and electromagnetic induction

A current-carrying wire creates a circular magnetic field around itself; the right-hand grip rule (thumb points along the current, fingers curl in the field's direction) gives the field's direction. Electromagnetic induction is the reverse idea: moving a magnet relative to a coil, or otherwise changing the magnetic flux through a circuit, induces an EMF and drives a current. Lenz's law says the induced current always flows in the direction that opposes the change causing it -- this is why you feel resistance pushing a magnet into a coil connected in a loop.