Units before everything

Every quantity in circuit analysis is an SI unit, and getting them right is half the battle.

• The six base units you meet here are the metre, kilogram, second, ampere (A), kelvin and candela.
• Circuit work leans on derived units: the coulomb (C), volt (V), ohm (Ω), farad (F) and watt (W).
• Prefixes scale them: k (10³), m (10⁻³), µ (10⁻⁶), so 12,500 Ω reads as 12.5 kΩ.

Charge, current, voltage

These three definitions are the vocabulary of every circuit that follows.

• Charge q is measured in coulombs; one electron carries 1.602 × 10⁻¹⁹ C, and charge is only ever transferred, never created or destroyed.
• Current is the rate of charge flow, i = dq/dt, so 1 A = 1 C/s. DC is constant; AC reverses sinusoidally.
• Voltage v = dw/dq is the energy per unit charge: the push. Its direction (the + and − signs) matters as much as its size.

Power and the passive sign convention

Power ties voltage and current together, and its sign tells you which way energy flows.

• Power p = vi in watts. Positive means the element absorbs; negative means it supplies.
• The passive sign convention: if current enters the + terminal, p = +vi; if it enters the − terminal, p = −vi. Get the terminals right and the signs follow.
• Conservation of energy: ∑p = 0 across the whole circuit: every watt supplied is a watt absorbed. This single check catches most arithmetic mistakes.

Elements and sources

Every part of a circuit is either delivering energy or shaping it.

• Active elements are the sources; passive elements are R, L, C.
• An independent source has a fixed value; a dependent source's value is set by another voltage or current (VCVS, CCVS, VCCS, CCCS): watch its controlling variable and its sign.
• Multisim lets you draw the circuit and read every V, I and P back with a DC Operating Point Analysis: solve by hand first, then let the tool confirm.