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Every circuit, from a torch to a train, obeys the same short rule: the current through a conductor depends on the voltage pushing it and the resistance holding it back. Ohm's law puts that in one line, and with a second formula for power you can answer most everyday electrical questions.
The three-way triangle
Cover the quantity you want and the other two show how to get it. Voltage is on top; current and resistance sit below.
- 1Find voltageV = I × R. A 0.5 A current through 10 Ω needs 5 V.
- 2Find currentI = V ÷ R. A 12 V supply across 4 Ω drives 3 A.
- 3Find resistanceR = V ÷ I. 9 V and 0.03 A means 300 Ω.
Use base units: volts, amps and ohms. Convert milliamps by dividing by 1,000 (20 mA = 0.02 A) and kilo-ohms by multiplying by 1,000.
Adding power
Power is how fast electrical energy is turned into heat, light or motion. Since V = IR, you can swap terms to write power in three useful ways, depending on which two numbers you know.
| You know | Power formula | Example |
|---|---|---|
| Voltage and current | P = V × I | 230 V × 8.7 A ≈ 2,000 W |
| Current and resistance | P = I² × R | 3 A and 4 Ω → 9 × 4 = 36 W |
| Voltage and resistance | P = V² ÷ R | 12 V and 4 Ω → 144 ÷ 4 = 36 W |
All three answers can agree. The 12 V, 4 Ω, 3 A circuit above uses 36 W by every route.
Worked example 1: an LED resistor
An LED needs a resistor in series, or it draws too much current and burns out. Suppose a 5 V supply, a red LED that drops about 2 V, and a target current of 20 mA.
- 1Voltage left for the resistor5 V − 2 V = **3 V**.
- 2ResistanceR = V ÷ I = 3 ÷ 0.02 = **150 Ω**.
- 3Power in the resistorP = V × I = 3 × 0.02 = **0.06 W**.
- 4Pick a partA 150 Ω, quarter-watt (0.25 W) resistor has plenty of margin.
If you cannot find 150 Ω, use the next higher standard value. A slightly higher resistance gives a slightly dimmer, cooler LED, which is safe.
Worked example 2: a 2,000 W kettle
A kettle is rated 2,000 W on a 230 V supply, the standard in India and much of the world. Rearranging P = V × I gives the current, and Ohm's law then gives the resistance of the heating element.
A 16 A socket is common for heavy appliances. Plug a kettle and a heater into the same extension board and the total can exceed what the cable allows.
Worked example 3: light bulbs
Higher wattage at the same voltage means more current and lower resistance. A thicker filament, not a thinner one, makes a brighter incandescent bulb.
| Bulb (230 V) | Current | Resistance when hot |
|---|---|---|
| 60 W | 0.26 A | 882 Ω |
| 100 W | 0.43 A | 529 Ω |
| 1,500 W heater | 6.52 A | 35.3 Ω |
Resistance of a filament rises as it heats, so a cold bulb measures much lower than these hot figures.
Current climbs in step with power when voltage is fixed. Heating appliances use by far the most.
Series and parallel resistors
Real circuits use more than one resistor. How you connect them decides how the values combine.
- Totals add: 100 + 220
- Same current through both
- Voltage splits between them
- 1/R = 1/100 + 1/220
- Smaller than the smallest resistor
- Same voltage across both
For two resistors in parallel, a handy shortcut is (R1 × R2) ÷ (R1 + R2) = 22,000 ÷ 320 = 68.75 Ω.
A voltage divider is a series pair used to get a smaller voltage. With a 9 V battery across 100 Ω and 220 Ω, the current is 9 ÷ 320 = 0.028 A. The voltage across the 220 Ω resistor is 0.028 × 220 = 6.2 V, and across the 100 Ω resistor 2.8 V.
Where the law stops being simple
- Non-ohmic parts. Diodes, LEDs and transistors do not have a fixed resistance. Their current does not rise in a straight line with voltage.
- Temperature. Metal resistance rises with heat, so a hot wire behaves differently from a cold one.
- AC circuits. With alternating current, coils and capacitors add reactance, and the law uses impedance instead of resistance.
- Real batteries. Voltage drops under load because of internal resistance.
Quick sanity checks
- Convert units first. Milliamps and kilo-ohms are the usual slip.
- Check the power rating of any resistor: P = I²R must be below its watt rating, with margin.
- Voltage drops add up around a loop to equal the supply voltage.
- Parallel total below the smallest. If yours is larger, recheck the calculation.
- Wire gauge matters. Higher current needs thicker wire to avoid heating.
Questions people ask
What is Ohm's law?
It states that voltage equals current multiplied by resistance, V = I × R. It describes how much current flows through a resistor for a given voltage.
How do I calculate current from power and voltage?
Divide power by voltage: I = P ÷ V. A 2,000 W kettle on 230 V draws about 8.7 amps.
What is the formula for electrical power?
P = V × I. Using Ohm's law you can also write it as P = I² × R or P = V² ÷ R.
How do I choose a resistor for an LED?
Subtract the LED's forward voltage from the supply voltage and divide by the desired current. For 5 V, a 2 V LED and 20 mA, the resistor is 150 ohms.
How do resistors add in parallel?
The reciprocals add: 1/R = 1/R1 + 1/R2. The total is always smaller than the smallest resistor. For 100 and 220 ohms it is 68.75 ohms.
Does Ohm's law work for all components?
No. It holds for ohmic parts such as ordinary resistors. LEDs, diodes and transistors have a current that does not rise in proportion to voltage.