Electrical quantities & circuit analysis
Charge, units & energy
Give every number a meaning before putting it in a formula.
Charge is measured in coulombs (C), current in amperes (A), and voltage in joules per coulomb (V). One ampere means one coulomb per second. Power is the rate of energy transfer in watts; energy accumulates in joules. A wire already contains charge carriers: components transfer energy rather than use up charge. Prefixes matter: milli is 10⁻³, micro is 10⁻⁶ and kilo is 10³.
Ohm’s law, series & parallel
Look at the connections, not how the drawing is arranged.
For an ohmic resistor, V = IR. In series, the same current passes through each resistor and their voltage drops add. In parallel, both ends of each branch connect to the same two nodes: the voltage is shared and branch currents add. A node is a set of electrically connected points, not necessarily a visible dot. Redraw the nodes before combining a complicated network.
Kirchhoff, loading & equivalent sources
Use conservation laws when series-and-parallel shortcuts stop working.
Kirchhoff’s current law balances currents at a node; the voltage law balances signed voltage rises and drops around a loop in a lumped circuit model. Pick current directions and a reference node, write independent equations, then solve. A negative answer means the actual direction is opposite your arrow. A linear two-terminal network can also be represented by a Thévenin voltage and series resistance, or a Norton current and parallel resistance.
Tolerance: when equal parts are not quite equal
Turn a nominal resistor ratio into a realistic output interval.
A tolerance is an allowed range, not a prediction of an individual part’s error. In a 5 V divider with two nominal 10 kΩ resistors, the nominal output is 2.5 V. The lowest output occurs with the upper resistor at its maximum and the lower at its minimum. Reverse those extremes for the highest output. Measure parts or choose tighter tolerance when the error budget needs it.