Ohm’s Law: How to Find Voltage, Current and Resistance

Ohm’s law links the three basic quantities in a circuit: voltage V (volts), current I (amps) and resistance R (ohms, Ω). If you know any two, you can find the third: V = I × R.

For learning and checking coursework only. Electrical work can kill. Follow the electrical code where you live and have a licensed electrician do or inspect real wiring.

Try it with your own problem ↓

The steps

Write down the two values you know and the one you want.
Change prefixes to base units: milliamps ÷ 1,000 = amps, kilohms × 1,000 = ohms.
Pick the form: V = I × R, I = V ÷ R, or R = V ÷ I. (Cover the one you want in the V-over-I-R triangle.)
Work it out and write the unit.
Check by going back the other way.

A worked example

A 9 V battery drives a current of 30 mA through a resistor. What is the resistance?

We know V = 9 V and I = 30 mA, and we want R.
Base units: 30 mA = 30 ÷ 1,000 = 0.03 A.
R = V ÷ I = 9 ÷ 0.03 = 300 Ω.
Check: I = 9 ÷ 300 = 0.03 A. ✓

The resistance is 300 Ω.

Why it works

Voltage is the push, current is the flow and resistance is how hard the path is. A bigger push gives more flow and a harder path gives less, so the current is the voltage divided by the resistance. Rearranging I = V ÷ R gives the other two forms.

Try it with your own problem

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Work it out: 9 V and 30 mA, resistanceOpens The Circuit Board with this example

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Common mistakes

Ignoring the prefix. 9 ÷ 30 = 0.3 is wrong, because 30 mA is 0.03 A.
Multiplying when you should divide. Only V = I × R multiplies. Current and resistance are each found by dividing the voltage.
Mixing up k and M. 4.7k is 4,700 Ω; 4.7M is 4,700,000 Ω.
Using it where it doesn’t fit. Ohm’s law describes resistors. A lamp’s resistance changes as it heats up, and an LED doesn’t follow it at all.

Questions people ask

What current flows with 12 V across 4 ohms?

I = V ÷ R = 12 ÷ 4 = 3 A.

How does power fit in?

P = V × I. For 9 V and 0.03 A, P = 0.27 W (270 mW). It can also be written P = I² × R or P = V² ÷ R.

What current does a 100 W bulb draw on 120 V?

I = P ÷ V = 100 ÷ 120 ≈ 0.83 A.

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