Most of a beginner circuit is one equation and a handful of consequences. Learn what the three quantities mean physically rather than as letters, and the rest follows — including why the LED you wired straight to a battery lasted about a second.
Ohm’s law, and what the letters actually are
V = I × R. Voltage equals current times resistance. The water analogy is imperfect but genuinely useful:
- Voltage (V, volts) — the pressure pushing charge along. A battery is a pump. Voltage is measured across two points, never at one.
- Current (I, amps) — how much charge is actually flowing. Measured through a point.
- Resistance (R, ohms) — how much the path fights the flow. A narrow pipe.
Rearranged: I = V / R and R = V / I. Nearly every beginner question is one of those three, and the Ohm’s law calculator solves for whichever you are missing.
Power matters too: P = V × I, in watts. This is what decides whether a component gets warm or gets destroyed, and it is the figure people forget to check. A resistor with the right resistance and the wrong power rating will still burn.
Why an LED needs a resistor
An LED is not a resistor. It does not obey Ohm’s law — below its forward voltage almost no current flows, and above it the current rises almost vertically. There is no self-limiting behaviour at all.
Connect a 2 V LED directly to a 5 V supply and the circuit has nothing left to drop the extra 3 V across. Current runs away, the junction overheats, and the LED fails — sometimes instantly, sometimes after minutes of looking fine, which is worse because it seems to have worked.
The resistor absorbs the difference. Size it like this:
R = (supply voltage − LED forward voltage) / desired current
For a red LED (about 2 V, 20 mA) on 5 V: (5 − 2) / 0.02 = 150 Ω. The next standard value up is 150 Ω or 220 Ω — always round up, since a larger resistor means slightly less current and a slightly dimmer LED, while rounding down means more current than intended.
Forward voltage varies by colour, which surprises people: red and yellow sit near 2 V, blue and white nearer 3 to 3.4 V. Swapping a red LED for a blue one without recalculating gives a noticeably dim result. The LED resistor calculator has the usual figures built in.
Reading a resistor
The bands encode the value. On a four-band resistor: the first two are digits, the third is how many zeros to add, and the fourth — separated by a gap, usually gold or silver — is the tolerance.
Brown, black, red, gold is 1, 0, then two zeros: 1000 Ω, or 1 kΩ, ±5%. Five-band resistors add a third digit for precision parts.
Two practical notes. Read from the end away from the tolerance band, or you will read the value backwards — and brown/red/orange are genuinely hard to tell apart under warm light, so check with a meter when it matters. The colour code calculator works in both directions.
Voltage dividers
Two resistors in series split the voltage between them in proportion to their resistance. Tap the junction and you get a fraction of the input:
V_out = V_in × R2 / (R1 + R2)
Two equal resistors give you half the input. This is how a sensor reading gets scaled into a range a microcontroller can read.
The trap: a divider is not a power supply. As soon as you draw meaningful current from the tap, the output voltage sags, because the load is effectively a third resistor in the network. Dividers are for signals and references, not for powering anything. The divider calculator works out the ratio and the resistor pair.
Series and parallel, in one line each
- Resistors in series add. Same current through each, voltage splits between them.
- In parallel the total is smaller than the smallest. Same voltage across each, current splits. Two equal resistors in parallel give half the value.
- Capacitors do the opposite — parallel adds, series reduces. This catches out anyone who learned resistors first.
Capacitors, briefly
A capacitor stores charge and resists changes in voltage. Two jobs cover most beginner use: smoothing a supply that dips when something switches on, and setting a time constant with a resistor.
That time constant is τ = R × C — the time to reach about 63% of the way to the final voltage, and roughly five of those to effectively arrive. It is the basis of simple timers and debouncing. The capacitor calculator handles series, parallel and time constants.
Four mistakes worth avoiding
- No resistor on an LED. The most common first mistake, and the LED does not survive it.
- Ignoring power ratings. Check P = V × I against the component’s rating. A quarter-watt resistor asked to dissipate a watt will smell distinctive.
- Measuring current like voltage. Voltage goes across a component with the meter in parallel; current goes through, with the meter in series. Putting an ammeter across a supply is a short circuit.
- Assuming the supply is exactly what it says. A “5 V” USB supply can sit anywhere from 4.75 to 5.25 V, and a 9 V battery reads about 9.5 V fresh and 7 V tired.