Electricity is analogous to fluid flow, as compared in the table below.

Fluid flows in pipes; electricity flows in electrical conductors, usually wires, circuit-board traces and components. What actually flows is electric charge, q, measured in coulombs (C). Current, i, is the rate of charge flow, or

That is, current is the change in charge flowing past a given point per change in time over which the change in charge was measured. Current is measured in units of amperes (A). One ampere is one coulomb per second. Resistance, R, determines how much current will flow when a voltage is placed across it. Voltage, v, has units of volts, V, and is an "across" quantity, like pressure and speed.

Current, flow and force are through quantities and are measured in the branches of a network (whether it be wiring or plumbing). Network nodes are connected by branches.

The most basic and often-used electrical equation is Ohm’s Law:

Two resistances in series are the equivalent of a single resistance with the sum of their values. Besides series connections, circuit elements can be connected in shunt or parallel, as shown for two resistors below:

The parallel resistances can be replaced with a single, equivalent resistance of the above value.

Besides Ohm’s Law, the most basic circuit principles are Kirchhoff’s two laws. Kirchhoff’s Voltage Law (KVL) states that the sum of the voltages around a closed loop must equal zero:

Applying KVL,

or, the sum of the voltage drops equals the voltage source:

V_S = V_R1 + V_R2

KVL is the analog of the principle that the sum of the pressure drops in a fluidic circuit equals the pressure source.

Kirchhoff’s Current Law (KCL) states that the sum of current into a node must equal zero:

In other words, charge does not accumulate in nodes. By convention, currents flowing into a node are negative and out of a node are positive. This is analogous to the principle that the sum of fluid flows into a junction must equal the flows out (for incompressible fluids). KCL is demonstrated by the following circuit:

Applying KCL,

i_out = i₁ + i₂

All current into the junction must leave it.

In systems theory (whether it be electronic, chemical, mechanical, thermal or aerodynamic), some quantities remain constant while others change. A constant or static quantity is "dc" and a changing or dynamic quantity is "ac." Historically, these electrical terms meant "direct current" and "alternating current," but "constant" and "changing" are better descriptions. An ac waveform can be added to a dc offset, as shown below:

The ac waveform is added to a dc amount that is the average of the (total) waveform. This average amount around which the ac component varies is the waveform’s dc component. Ac and dc are often used to refer to the kind of voltages available from sources. Batteries are "dc" in that the voltage across their terminals is constant. Diesel-driven generators put out a sinusoidal ("sinewave") voltage that has a frequency of typically 60 Hz. Because it is a sinewave, its voltage reverses (is bipolar), reaching positive and negative peaks 60 times per second.

Some electronic components are inherently dynamic or "ac" in their behavior. The basic dynamic circuit elements are capacitors and inductors. Together, they are called reactive (versus resistive) elements. Transformers are a variation on inductors. Transistors, integrated circuits, switches, lamps and connectors are not basic circuit elements, but can be modeled by equivalent circuits that can include reactances, resistances and controlled sources.

Frequency, f, is the rate a periodic waveform repeats. The unit is Hertz (Hz), which is "per second." North American electrical power has a frequency of 60 Hz. The reciprocal of frequency is period, T:

T = 1/f

Frequency counter/timers are instruments that measure frequency, period, and other time-related aspects of periodic waveforms. Deluxe digital multimeters have frequency measurement capability, as do most newer digital and some analog oscilloscopes.

A very common circuit used to reduce or scale a voltage is a voltage divider. It consists of 2 resistors and has an input and output. The common terminal shared by input and output is grounded in the diagram below. (Note the ground symbol.)

Voltage measurements are made relative to ground unless otherwise noted. In general, the common terminal of the divider need not be at 0 V.

The general circuit for a voltage divider, with common node at ground, is shown below.

The input loop has three series elements: v_in (source), R₁ and R₂. Applying KVL results in:

v_in = v_R1 + v_R2

At the output loop, the sensed voltage, v_out, is:

v_out = v_R2

Then the ratio of output to input voltage (the scale-factor) is:

The voltages on the right side of this equation can be expressed in circuit element values by applying Ohm’s Law. Let the input-loop current be i. Then

Also by Ohm’s Law,

i = v_in/(R₁ + R₂)

Substituting and simplifying,

This is the basic voltage-divider equation. It expresses the scale-factor or attenuation of voltage from input to output. The input nodes (input and common) are the pair of terminals across which the input voltage occurs. Such a pair is called a port. The output port has v_out across its pair of terminals. By convention, current flowing into a port + terminal is positive.

A current divider scales current in the R₂ branch of parallel resistors with input current of i_in to the parallel pair. Then i_out  = i₂ and the current-divider formula (solved using KCL) is:

Current dividers attenuate current. Note that R₁, not R₂, is in the numerator.

Thevenin’s theorem is a way of simplifying circuits with (independent) sources to that of a single voltage source in series with a Thevenin equivalent resistance. This is the same equivalent circuit that was used earlier to model actual voltage sources. In general, an arbitrary circuit, as shown below, has a Thevenin equivalent circuit, shown to the right. The Thevenin voltage source and resistance can be found as follows. The Thevenin voltage is found by leaving the output port open.

No current will flow through R_th and

v_th = v_oc

where v_oc is the output open-circuit voltage. The Thevenin resistance is found by shorting the output and measuring the resulting output short-circuit current, i_sc..

Then

R_th = v_th/i_sc

Analytically, v_oc and i_sc are found by applying the basic circuit principles: Ohm’s Law, KVL and KCL. Empirically, open-circuit voltage and short-circuit current are measured at the output.

Norton’s theorem reduces the same kind of arbitrary network to a Norton equivalent circuit: a current source, i_n, in parallel with a Norton equivalent resistance, R_n. A Norton equivalent circuit can be derived by finding the Thevenin circuit. Then the Norton values are:

i_n = v_th/R_th R_n = R_th

Linear circuits (such as the above) with multiple sources can be solved for voltages and currents by solving the circuit for one source at a time while nulling (setting to zero) the others: voltage sources are shorted and current sources are opened. Add the results from each solution for each node (voltages) and branch (currents) to get the combined (total) result. Ideal voltage sources have zero resistance (shorted); ideal current sources have infinite resistance (open).

The superposition of these voltages results in

Then

in agreement with the parallel-resistor result.

The Norton equivalent circuit is readily calculated from the Thevenin circuit and is shown below. The source symbol is that of a current source.

where

The most basic electronic test and measurement instrument worth owning is the digital multimeter (DMM). For about $100, a meter (such as a Beckman DM27XL or equivalent, for about $60) measures voltage, current, resistance and other quantities (frequency, capacitance) and tests transistors and diodes. On low-resistance ranges, continuity (electrical connection of wires) can be tested by an audible beep.

A big step up from a DMM is an oscilloscope, which plots a graph of input (probe) voltage versus time. A ‘scope is a "window" into dynamic (changing-in-time) circuit behavior. Voltage and time scales are adjustable ("volts/div and "time/div").

The ‘scope screen is like a window, and can only show a segment of the ongoing voltage function (or waveform) in time. Some way of selecting the alignment of this displayed window in time is needed. The trigger system is used to start the trace on the screen at the same point on a repetitive waveform for each sweep of the beam across the face of the screen. By tracing out the same waveform each time, the displayed trace looks stable. When the triggering is not correctly adjusted, many different traces are drawn, showing an unstable display. Trigger source, mode, slope and level controls are adjusted to make the trace stable. Instability is usually due to the trigger level being set to outside the maximum bounds of the waveform on "normal" triggering mode. "Auto" mode keeps the trace going (to show the no-waveform baseline of 0 V) and is generally the most useful mode. When viewing waveforms of less than 50 Hz, however, normal mode is necessary for stability.

Oscilloscopes come in two major categories nowadays: analog and digital. Analog ‘scopes are unable to capture transient (one-time) waveforms but are low-cost and show a continuous waveform. Digital storage oscilloscopes (DSOs) now sell for under $1000 and are able to capture (or "store") single-shot events by sampling the input waveform at points in time, resulting in a discrete (not continuous) display. Transient capture is useful for rocketry since firing events are not repetitive. DSOs are a kind of data acquisition system with a front-panel instead of a computer as interface.

Another useful test instrument is the power supply. Supplies are required as subsystems in electronic equipment, but a general-purpose test-bench supply, with multiple outputs, including one or more with variable output voltage, can expedite system testing.