Electric Circuits

A circuit is a closed loop where charge flows. Three core quantities describe any circuit:

• Current $I$: rate of charge flow in amperes ($C/s$). Conventional current moves from high to low potential.
• Voltage $V$: potential difference driving current, measured in volts.
• Resistance $R$: opposition to current flow, measured in ohms.

These are tied by Ohm's law: $V = I R$. Rearranged as $I = V/R$, current equals voltage divided by resistance. The power dissipated as heat is $P = IV = I^2 R$, which is why active electronics get hot.

Combining Components

Components wire in two basic ways:

For two parallel branches, $R = \frac{R_1 R_2}{R_1 + R_2}$. Adding parallel paths decreases total resistance.

Common Pitfall: Swapping rules. In series, resistances add (total goes up). In parallel, total resistance is smaller than the smallest branch. Also remember $I = V/R$: more resistance means less current.