Circuit Basics

Voltage, current, resistance and power, Ohm’s law, series and parallel circuits, dividers, Kirchhoff’s laws, DC and AC, and how to read a schematic.

On this page

Voltage, current, resistance and power
Ohm’s law and power
Series and parallel
Voltage dividers
Kirchhoff’s laws
DC and AC
Reading a schematic
FAQ

Voltage, current, resistance and power

Every circuit moves electrical charge around a loop. Four quantities describe it. A water pipe is a useful picture: voltage is the pressure that pushes, current is the flow, resistance is a narrow section that restricts the flow, and power is the rate at which energy is delivered (and, in a resistor, turned into heat).

Quantity	Symbol	Unit	What it means
Voltage	V (or E, U)	volt, V	Electrical pressure between two points; always measured between two points
Current	I	ampere, A	Flow of charge past a point; 1 A is 1 coulomb per second
Resistance	R	ohm, Ω	Opposition to current; a short wire is near 0 Ω, air is nearly infinite
Power	P	watt, W	Rate of energy use: P = V × I; 1 W is 1 joule per second
Energy	E	joule, J (or watt-hour, Wh)	Power over time; a 3.7 V 2 000 mAh cell holds 7.4 Wh
Frequency	f	hertz, Hz	Cycles per second of an alternating signal

By convention, conventional current flows from the positive terminal, around the circuit, to the negative terminal. The electrons that actually carry it move the other way, but every formula and symbol uses the conventional direction.

Prefixes

Prefix	Symbol	Multiplier	Example
pico	p	10⁻¹²	22 pF capacitor
nano	n	10⁻⁹	100 nF capacitor
micro	µ	10⁻⁶	10 µF capacitor, 50 µA
milli	m	10⁻³	20 mA LED current
kilo	k	10³	4.7 kΩ resistor
mega	M	10⁶	1 MΩ resistor, 16 MHz clock
giga	G	10⁹	2.4 GHz radio

Ohm’s law and power

V = I × R I = V ÷ R R = V ÷ I

P = V × I = I² × R = V² ÷ R

Ohm’s law links the three: the current through a resistor is proportional to the voltage across it. Put any two of V, I and R in and the third follows. The power formulas tell you how hot a part will run, which sets the power rating you need.

Worked example: 12 V across a 470 Ω resistor

Current: I = 12 ÷ 470 = 25.5 mA.
Power: P = 12 × 0.026 = 0.31 W.
A ¼ W resistor would overheat. Keep the dissipation at half the rating or less, so choose a 1 W part (or reduce the voltage).

Series and parallel

The same two resistors in series and in parallel across 12 V. In series the current is the same everywhere and the voltages add; in parallel the voltage is the same and the currents add.

Combination	Total resistance	Rule of thumb
Series	R₁ + R₂ + …	Same current through each; voltages add up to the supply; the total is larger than the biggest
Parallel	1 ÷ (1 ÷ R₁ + 1 ÷ R₂ + …)	Same voltage across each; currents add; the total is smaller than the smallest
Two in parallel	R₁ × R₂ ÷ (R₁ + R₂)	Two equal resistors give half; 1 kΩ and 3 kΩ give 750 Ω

Lamps, LEDs, loads and sockets on a power rail are in parallel, so each gets the full supply voltage and the supply must provide the sum of all currents. A string of fairy lights wired in series shares the voltage, and one failure breaks the whole string.

Voltage dividers

V_out = V_in × R₂ ÷ (R₁ + R₂)

An LED with its series resistor, and a voltage divider.

Worked example: LED and divider

LED: a red LED drops about 2.0 V and should run at 10 mA from 5 V. R = (5 − 2.0) ÷ 0.010 = 300 Ω; the nearest standard value is 330 Ω, giving I = 3.0 ÷ 330 = 9.1 mA. The resistor dissipates 3.0 V × 9.1 mA = 27 mW, far below the rating of a ¼ W resistor.
Divider: R₁ = 1 kΩ, R₂ = 2 kΩ from 5 V gives 5 × 2 ÷ 3 = 3.33 V, with no load. It carries 5 ÷ 3 000 = 1.7 mA in itself.
Loading: connect a 10 kΩ load across R₂. The two are in parallel (1.67 kΩ), so V_out = 5 × 1.67 ÷ (1 + 1.67) = 3.13 V. The load pulled the output down by 0.21 V.
A divider works well only when the load draws much less current than the divider itself (a tenth or less). It suits an input pin that draws almost nothing; it is a poor way to supply power.

Kirchhoff’s laws

Current law (KCL). The currents into any junction add up to the currents out of it. Charge does not pile up. In the parallel circuit above, 12 mA + 4 mA leave the supply and split into 12 mA and 4 mA.
Voltage law (KVL). Going around any closed loop, the voltage rises and drops add up to zero. In the series circuit, the 12 V supply equals 3 V + 9 V across the two resistors.

Between them, these laws solve any circuit. In practice, write down what you know (supply voltage, resistor values), find the total resistance, find the current, then work out the voltage across each part.

DC and AC

Direct current (DC) flows one way at a steady voltage: batteries, USB power and the supplies inside every electronic device. Alternating current (AC) reverses direction regularly, which is what the wall socket delivers. Mains is about 120 V at 60 Hz in North America and 230 V at 50 Hz in much of the rest of the world.

One cycle of a mains sine wave takes 16.7 ms at 60 Hz. The RMS value (120 V) is the DC voltage that would give the same heating.

V_RMS = V_peak ÷ √2 ≈ 0.707 × V_peak T = 1 ÷ f

Meters and the nominal values (120 V, 230 V) quote RMS. The peak is higher: 120 V RMS peaks at 170 V, and 230 V RMS at 325 V. Capacitors and insulation must handle the peak.
A transformer works only on AC; a rectifier and filter capacitor turn AC into DC (see Diodes and LEDs).
Mains voltage kills. Do not work on live mains equipment, and see Workshop Safety before building anything connected to the wall.

Reading a schematic

A schematic shows how parts are connected, not where they sit. Every part has a standard symbol and a label made of a letter and a number.

The symbols for the parts covered in this guide. Variants exist (the resistor may be drawn as a plain rectangle in IEC drawings).

Letter	Part	Example
R	Resistor	R1 = 330 Ω
C	Capacitor	C3 = 100 nF
L	Inductor	L1 = 10 µH
D	Diode or LED	D2 = 1N4007
Q	Transistor	Q1 = 2N2222
U	Integrated circuit	U1 = LM358
SW, S	Switch	SW1 = power
J, P	Connector	J1 = USB-C
F	Fuse	F1 = 2 A
K	Relay	K1 = 5 V coil

Layout convention: power at the top, ground at the bottom, signals flowing left to right. Follow a signal from input to output.
Dots and crossings. A dot where lines meet is a connection. Lines that cross with no dot are not connected. (A small hop or arc also means no connection.)
Net labels. A name on a wire (such as +5V or SCL) connects every wire with the same name, even on different parts of the page. Ground symbols all connect to the same ground.
Pin numbers are on the chip symbol; check them against the datasheet, because a symbol does not show the physical order of the pins.

Electronics Fundamentals: the overview of this guide.
Resistors: the color code, standard values and power ratings.
Capacitors: how capacitors charge, filter and decouple.
Soldering: turning a circuit into something permanent.

FAQ

What is the difference between voltage and current?

Voltage is the push between two points; current is the flow that results. A battery has a voltage even when nothing is connected, but current flows only when there is a complete loop. A high voltage with a tiny possible current (static electricity) can be harmless, while a modest voltage with a large available current (a car battery) can start a fire.

What is ground?

Ground is the 0 V reference that every other voltage is measured against. In a battery circuit it is just the negative terminal. In a mains system, “earth” is also a safety connection to the ground. The two are not always the same thing, so check which one a drawing means.

Does current take the path of least resistance?

It takes all paths, in proportion to their conductance. Through two parallel resistors, more current flows through the smaller one, but some flows through the larger one too.

Why do batteries have an amp-hour rating instead of watts?

A battery’s voltage is roughly fixed by its chemistry, so its stored charge (mAh or Ah) tells you how long it can supply a given current. Multiply by the voltage to get energy in watt-hours.

How do I know what resistor rating I need?

Calculate P = I² × R (or V² ÷ R) and choose a part rated at twice that or more. See Resistors for standard ratings.

References

Horowitz, P. and Hill, W., The Art of Electronics, 3rd ed., Cambridge University Press: chapters 1 and 2.
Platt, C., Make: Electronics, 3rd ed., Make Community.
IEEE Std 315 and IEC 60617, graphical symbols for electrical and electronics diagrams.
IEC 60038, IEC standard voltages (nominal mains voltages).

Last reviewed: October 2026. Values are typical: check the datasheets of the parts you use. Do not work on live mains equipment unless you are qualified.