Circuit Analysis (DC & AC Steady State)

V = I·R, where V is voltage across an element (volts), I is current through it (amperes), and R is resistance (ohms). It applies to linear, ohmic resistors.

P = V·I = I²·R = V²/R. All three forms are equivalent for a resistor by Ohm's law, and the power is dissipated as heat.

The algebraic sum of all voltages around any closed loop in a circuit equals zero. Equivalently, the sum of voltage rises equals the sum of voltage drops around the loop.

The algebraic sum of currents entering any node (or closed boundary) equals zero. Equivalently, the sum of currents in equals the sum of currents out at a node.

Conservation of electric charge — charge cannot accumulate at a node in steady state, so current in must equal current out.

Add them directly: R_eq = R1 + R2 + ... + Rn. Series resistors carry the same current, and the equivalent is always larger than any single resistor.