Three quantities, one equation, and most of a first-year syllabus falls out of it. It is worth being genuinely fluent here, because every other calculation in electronics leans on it.
V = I x R
- V is voltage, in volts (V) — the push, always measured between two points
- I is current, in amperes (A) — the flow, always measured through something
- R is resistance, in ohms — how much the path opposes that flow
A worked example
5 V across a 220 ohm resistor. How much current flows?
I = V / R = 5 / 220 = 0.0227 A = 22.7 mA
Turn it round. You need 10 mA from a 9 V supply, so what resistor?
R = V / I = 9 / 0.010 = 900 ohms
900 is not a value you can buy, so you fit 1k — the nearest preferred value — and get 9 mA. Say that out loud in a viva rather than hiding it: choosing a stocked value and stating the resulting current is engineering, and quoting 900 ohms is not.
Ohm's law calculator
Open on its own pageFill in any two and the rest follow. It also tells you whether a quarter-watt resistor will survive it.
Fill in any two. Clear a box to solve for it.
Power: the part that gets forgotten
Ohm's law tells you the current. It does not tell you whether the resistor survives. Every resistor turns the energy it drops into heat, and every resistor has a rating — usually a quarter of a watt in a project kit.
P = V x I = I² x R = V² / R
- P is power, in watts (W)
- Use whichever form matches the two things you already know
That 220 ohm resistor on 5 V, carrying 22.7 mA:
P = V x I = 5 x 0.0227 = 0.11 W
A quarter-watt part is fine, running at under half its rating. Now try the same resistor on 24 V:
P = V² / R = 576 / 220 = 2.6 W
Ten times the rating. It will scorch the board, drift high in value, and eventually go open circuit. Note how the voltage went up by about 5 and the power by 26 — power goes with the square of voltage, which is why circuits that are comfortable on 5 V destroy themselves on 24 V.
Series and parallel
In series — one path, end to end — the same current goes through every part, and the resistances add.
R_total = R1 + R2 + R3 ...
In parallel — several paths side by side — every part sees the same voltage, and the conductances add, so the total is always lower than the smallest one.
1 / R_total = 1 / R1 + 1 / R2 + ...
- For exactly two: R_total = (R1 x R2) / (R1 + R2)
- For N equal resistors: R_total = R / N
| Arrangement | Result | Check |
|---|---|---|
| Two 10k in series | 20k | Bigger than either |
| Two 10k in parallel | 5k | Half of one of them |
| 10k and 1k in parallel | 909 ohms | Just under the smaller one |
| 10k and 10 ohms in parallel | 9.99 ohms | The small one dominates completely |
If a parallel answer comes out larger than the smallest resistor in the group, the arithmetic is wrong. That check has caught more exam errors than any other.
The voltage divider
Two resistors in series across a supply, with the output taken from the middle. It is how a sensor gets read, how a 5 V signal is dropped to the 3.3 V an ESP32 will tolerate, and how a potentiometer works.
Vout = Vin x R2 / (R1 + R2)
To get 3.3 V from 5 V: the ratio needs to be 0.66, and R1 = 1k with R2 = 2k gives 5 x 2/3 = 3.33 V. In practice you use 1k and 2k, or 10k and 20k — the ratio sets the voltage, not the individual values.
So why not always use 1M and 2M and waste no current? Because whatever you connect to the output sits in parallel with R2 and changes the ratio. Keep the divider's current at least ten times whatever the load draws. For a microcontroller input pin, resistors in the 1k to 100k range are the usual compromise between wasted current and being pushed around by the load.
Voltage divider calculator
Open on its own pageThe ratio sets the voltage. This also shows the current the divider wastes doing it.
Whatever you connect to the output changes it. The load sits in parallel with R2, so keep the divider's own current at least ten times what the load draws. A divider cannot power a motor, a relay or a servo — for a lower supply rather than a lower signal, use a regulator.
Prefixes, and getting them right
| Prefix | Means | Example |
|---|---|---|
| p (pico) | x 0.000 000 000 001 | 22 pF |
| n (nano) | x 0.000 000 001 | 100 nF |
| u (micro) | x 0.000 001 | 10 uF, 500 uA |
| m (milli) | x 0.001 | 20 mA, 5 mV |
| k (kilo) | x 1 000 | 10 k |
| M (mega) | x 1 000 000 | 1 M, 16 MHz |
Capital M is mega, lowercase m is milli, and they are a billion apart. On a schematic 1M is a megohm resistor.