First Circuits: Your First Working Electronics
Move from the core idea to a real, measurable circuit — a battery, a resistor and an LED on a breadboard, checked with a multimeter. No prior electronics assumed; every calculation has a hands-on tool you can try.
You'll move from the core relationship (Ohm's Law) to building and measuring a real circuit. Each module has a short explanation, a worked example, a reference table and an interactive tool, so you can try the maths even before you touch the hardware.
A solderless breadboard, a few resistors (150–470 Ω), one or two LEDs, jumper wires, a 9 V battery or a 5 V supply, and a basic multimeter. The tools below let you practise without the parts.
1. Ohm's Law — the relationship that runs everything
Every circuit you'll ever build rests on one relationship between three quantities: voltage, current and resistance. Voltage (V, volts) is the electrical "pressure" that pushes charge around a loop — the squeeze on a water balloon. Current (I, amperes or "amps") is the actual flow of charge — how much water moves per second. Resistance (R, ohms, Ω) is how hard the circuit fights that flow — a narrowing in the pipe. Georg Ohm showed in 1827 that these three are locked together in a single equation, and it still describes nearly every electronic circuit you'll touch.
The equation is V = I × R: the voltage across a component equals the current through it multiplied by its resistance. Because it's plain algebra you can rearrange it to find whichever value you're missing — current is voltage divided by resistance (I = V/R), and resistance is voltage divided by current (R = V/I). The "Ohm's triangle" is a memory aid: V on top, I and R on the bottom; cover the value you want and the two you can see tell you the operation (side‑by‑side = multiply, stacked = divide).
Make it concrete. Put a 9 V battery across a 470 Ω resistor: the current is I = V/R = 9/470 ≈ 0.019 A, or 19 mA. Now see how each "knob" moves the needle. Raise the voltage to 18 V and the current doubles to about 38 mA (current is directly proportional to voltage). Swap the 470 Ω resistor for a 1 kΩ one and the current falls to 9 mA (current is inversely proportional to resistance). That last point is the most useful intuition in all of electronics — resistance is how you control current — and it's exactly why the LED module always starts with a resistor.
Enter two values to solve for the third.
| Quantity | Symbol | Unit | Symbol | Water analogy |
|---|---|---|---|---|
| Voltage | V | volt | V | Pressure |
| Current | I | ampere | A | Flow rate |
| Resistance | R | ohm | Ω | Pipe narrowing |
Mixed units. A "kΩ" is a thousand ohms and a "mA" is a thousandth of an amp. The most frequent beginner error is mixing milliamps with amps — a factor of 1,000 off. Convert everything to base units (volts, amps, ohms) before calculating, then convert the answer back for the label.
2. Resistors — controlling the flow
A resistor is a component that opposes current by a fixed amount, measured in ohms. In practice resistors are the workhorses of circuits: they limit how much current a component receives, split a voltage into smaller values, set a transistor's bias point, pull a signal line to a known level, and divide sensor signals. You will not build a single useful circuit without them. Because a resistor obeys Ohm's Law, the current through it is set entirely by the voltage across it and its resistance — which is precisely why you can use one to decide exactly how much current an LED or other device gets.
Resistor values use prefixes: "220" is 220 Ω, "4.7 k" is 4,700 Ω (k = kilo = 1,000), and "1 M" is 1,000,000 Ω (M = mega = 1,000,000). The physical part encodes its value with coloured rings — most are 4‑band: the first two bands are significant digits, the third is the multiplier (how many zeros), and the fourth is the tolerance. Tolerance is the manufacturer's accuracy guarantee: a ±5% resistor rated 100 Ω can actually be anywhere from 95 to 105 Ω, while a ±1% one sits within 99–101 Ω. For most beginner circuits ±5% is fine, but timing and reference circuits usually want ±1% or tighter. Resistors also carry a power rating (commonly ¼ W); push too much power through and they overheat, drift or burn out.
| Band | Role | Colours and values |
|---|---|---|
| 1st | 1st digit | Black 0 · Brown 1 · Red 2 · Orange 3 · Yellow 4 · Green 5 · Blue 6 · Violet 7 · Grey 8 · White 9 |
| 2nd | 2nd digit | (same as 1st band) |
| 3rd | Multiplier | Black ×1 · Brown ×10 · Red ×100 · Orange ×1k · Yellow ×10k · Gold ×0.1 · Silver ×0.01 |
| 4th | Tolerance | Brown ±1% · Red ±2% · Gold ±5% · Silver ±10% |
Reading example: bands Brown – Black – Red – Gold are 1, 0, ×100, ±5% → 10 × 100 = 1,000 Ω = 1 kΩ ±5%. Now the current‑limiting idea in action: a sensor output must be limited to 5 mA from a 5 V rail, so the series resistor is R = V/I = 5/0.005 = 1,000 Ω = 1 kΩ (a standard value, so you're done). Always pick from a standard series (E12 or E24) and always check the power it will dissipate — P = V·I, or P = I²·R — against its rating. A ¼ W part comfortably handles a few hundred milliwatts, which covers nearly every beginner project.
Resistor colour‑code decoder (4‑band)
| Ω | Ω | kΩ | kΩ |
|---|---|---|---|
| 100 | 470 | 1.0 | 4.7 |
| 150 | 560 | 1.2 | 5.6 |
| 220 | 680 | 1.5 | 6.8 |
| 330 | 820 | 2.2 | 10 |
(1) Reading the bands from the wrong end — start at the end nearest the tolerance band (the wider gold/silver/brown ring, set slightly further from the edge). (2) Ignoring power rating in high‑current paths. If a resistor glows or smells, it's dissipating too much power — use a higher‑wattage part or a higher resistance.
3. LEDs — light that only flows one way
An LED (light‑emitting diode) glows when current flows through it in the forward direction — and does nothing (or worse) if you push current the other way. That one‑way behaviour is why polarity matters. The anode (the + terminal, usually the longer lead) must connect toward the positive side of the supply, and the cathode (the − terminal, the shorter lead, marked by a flat notch on the case's edge) toward the negative side. Backwards, the LED simply won't light; forcing large reverse voltage can damage it. On a breadboard you'll often see a diode symbol beside the LED holes — the triangle points the "allowed" direction, anode to cathode, exactly like the one in the circuit above.
Two numbers define how you drive an LED. The forward voltage (Vf) is the voltage the LED "uses up" when lit — roughly 1.8–2.2 V for red and infrared, 2.0–2.4 V for yellow/classic green, and 3.0–3.5 V for blue and white. The other is the forward current: a typical small LED is rated for 20 mA continuous, and too little makes it dim while too much burns it out. Because most supplies sit well above the LED's Vf, you almost always put a current‑limiting resistor in series. The resistor absorbs the leftover voltage and sets the current with Ohm's Law: R = (Vsupply − Vf) ÷ I.
Worked example: a red LED (Vf ≈ 2.0 V) from a 5 V supply at 20 mA. R = (5 − 2.0) ÷ 0.020 = 3 ÷ 0.020 = 150 Ω. 150 Ω is a standard value, so you could use it; many designers round up to 180 Ω or 220 Ω to keep the current safely at or under 20 mA (with 220 Ω the current is (5−2)÷220 ≈ 13.6 mA — comfortably safe and still bright). At 9 V the same math gives (9 − 2) ÷ 0.020 = 350 Ω → use 360 Ω or 390 Ω. The pattern never changes: subtract the LED's Vf from the supply, divide by your target current, and pick the next standard resistor at or above the result.
LED resistor calculator
| Colour | Typical Vf | Typical max current |
|---|---|---|
| Red / infrared | 1.8 – 2.2 V | 20 mA |
| Yellow | 1.9 – 2.1 V | 20 mA |
| Green (classic) | 2.0 – 2.4 V | 20 mA |
| Blue / white | 3.0 – 3.5 V | 20 mA |
The three LED failures that catch everyone: (1) no resistor — the LED draws far more than 20 mA and dies, often after a bright flash. (2) reversed polarity — no light; swap the leads (the diode symbol shows the right way). (3) supply too close to Vf — the resistor ends up tiny and a small supply swing swings the current wildly. If an LED is dim, check polarity first, then confirm the resistor isn't one value too big, then measure the supply — it may not be what you think (that's the multimeter module).
4. Breadboards — wiring without solder
A solderless breadboard lets you build and rebuild circuits by pushing component leads into holes — no solder, no permanent traces. Under the plastic top are rows of springy metal clips: the holes in any one horizontal row are electrically joined by the strip beneath, so a component whose two leads land in the same row shares one node, and a component straddling two rows connects those two rows. A raised groove runs down the middle (the "ditch"), splitting the board into two halves — a reminder that rows on one side do not connect to rows on the other, and the place where wide ICs sit straddling the groove.
There are three kinds of connection. In the centre are the terminal strips: short rows of five holes each, in two banks (top and bottom) separated by the groove — each five‑hole row is one connection. Along the two long edges are the power rails, usually colour‑coded with a red stripe for the positive supply and a blue or black stripe for negative/ground. Critically, most breadboards have a gap in the middle of each rail, so the left and right halves of a rail are not automatically connected — you must bridge the gap with a jumper wire if you want the whole rail live. Columns run vertically and tie these together through components and jumpers.
Click (or focus + Enter) any group of holes to see what is connected.
The basic pattern for a two‑terminal part is simple: push one lead into one row and the other lead into a different row — those two rows are now joined through the component. To route a connection between two distant points, drop a short jumper wire into a spare row, or run a wire from one point into a row and another from that same row to the second point. When you add an IC, straddle it across the centre groove so each pin reaches a different row, then route its power and ground pins out to the rails. Build a habit of leaving a few empty rows as grab‑able "buses" for jumpers — it keeps the board readable and gives you room to fix mistakes.
| Location | Connected? | Note |
|---|---|---|
| One centre row (5 holes) | Yes — all five | One node per row |
| Across the centre groove | No | Top bank ≠ bottom bank |
| Power rail, one side of the gap | Yes — along that side | Continuous on one side |
| Power rail, across the gap | No (usually) | Bridge with a jumper |
| Same column, top ↔ bottom | No | A column is not a connection |
(1) Assuming a power rail is continuous across the middle gap — it usually isn't, so your "same" supply is actually two isolated nodes. (2) Trusting that two holes look connected but aren't — only holes in the same row, or the same unbroken rail segment, share a node. (3) A floating wire that has slipped out of its clip — it looks fine but is open. (4) An accidental short where one jumper ties + supply straight to ground — the battery or regulator warms up and a meter reads a short. When a circuit "should work" but doesn't, trace the physical connections hole by hole before blaming the components.
5. Your first multimeter skills
A multimeter is a handheld instrument that measures electrical quantities — voltage, current, resistance and continuity — and it's the single most valuable tool for learning why a circuit does or doesn't work. Most have a rotary dial that selects the mode and range, a set of input jacks (a "COM" jack for the black probe, a "VΩ" jack for voltage/resistance with the red probe, and one or more current jacks for the red probe in current mode), and a display. Learn the dial and the jacks before touching anything: the mode you select and the jack you plug into must match what you're measuring, or you'll get a bad reading or a blown fuse. The two probes are just coloured extensions of the leads — black to COM, red to the measurement jack.
The single most important concept is the difference between measuring voltage and current. Voltage is measured across two points (in parallel with what you're measuring): the meter sits between the two points and, having very high internal resistance, draws essentially no current and doesn't disturb the circuit. Current is measured through a point (in series): you break the circuit and put the meter in the path so the current flows through it; it has very low internal resistance so it adds little opposition. Confusing these is the classic mistake — put a meter in current mode across a live voltage source and you've made a near‑short, and the fuse blows (or worse). Rule of thumb: voltage = parallel (across); current = series (through).
To measure a battery's voltage: select DC voltage (V with a straight line and dashes, "V⎓"), put the red probe in the VΩ jack and black in COM, and touch the probes to the battery's + and − terminals — the display reads near 1.5 V (or 9 V), and a minus sign just means the probes are swapped. To measure a resistor: select ohms (Ω), remove it from the circuit (a powered circuit gives a nonsense reading and can damage the meter), and touch the probes to its two leads. Continuity is a resistance mode with a beep: when the resistance between the probes is very low (a closed path), it sounds a tone — perfect for checking that a wire or solder joint actually connects. Keep safety simple at these voltages: start on the highest range and step down, keep one hand free, and never measure mains AC with a meter not rated for it.
Pick what you're measuring
| Mode (dial) | Measures | Connect | Typical use |
|---|---|---|---|
| DC voltage (V⎓) | Voltage | Parallel, across two points | Battery, supply, drop across a part |
| AC voltage (V~) | Voltage | Parallel, across two points | Mains, AC signals |
| DC current (A⎓) | Current | Series, in the path | How much a load draws |
| Resistance (Ω) | Resistance | Across a de‑energised part | Check a resistor, open/short |
| Continuity (beep) | Closed path | Across a wire or joint | Find breaks and shorts |
| Task | Mode | Probe placement | Expected reading |
|---|---|---|---|
| 9 V battery | DC V | Red to +, black to − | ≈ 9.0 V |
| 220 Ω resistor (out of circuit) | Ω | Across the two leads | ≈ 220 Ω |
| Jumper wire | Continuity | Across both ends | Beep, ≈ 0 Ω |
| 5 V rail load | DC A | In series — break the rail | Load current (mA) |
Non‑negotiables: (1) For current, the meter must be in the path (series) with the red probe in a current jack — measuring current in the VΩ jack across a voltage source creates a short. (2) Start on the highest range when you don't know the value, then step down. (3) A blown fuse reads "OL" or "1" in current mode — power off, swap the fuse, re‑check the wiring. (4) Never apply the meter to mains AC unless it's explicitly rated for it. (5) When in doubt, measure voltage first — it's the safe, parallel, non‑disruptive measurement — before reaching for current mode.
Now build it
Bring the five modules together: set a 9 V battery on a breadboard, add a 390 Ω resistor and a red LED (anode toward +, cathode through the resistor to −), and use the multimeter to confirm the supply, the resistor value (out of circuit) and that the LED drops about 2 V across it. If the LED is dark, you now have a checklist — polarity, resistor value, rail connections, and a live supply — to work through methodically.
Ready for AC, filters and op‑amps? Continue to the next learning path from the Learn Electronics hub, or browse the calculator directory for the LED and Ohm's Law tools when they launch.
All figures and values here are standard teaching values for small‑signal parts; always confirm the exact ratings on the datasheet of the specific components you use.