Ohm's Law (V = IR)

Ohm's Law (V = IR) explains how voltage, current, and resistance relate in any circuit. This guide covers the formula, its three rearrangements, two worked examples, and the kind of component it doesn't apply to.

1.0 Introduction

If you only ever memorise one formula in electronics, make it this one. Ohm's Law links the three quantities you meet in almost every circuit, voltage, current, and resistance, and the deal it offers is simple: give it any two, and it hands you the third. That is enough to size a resistor, predict a current, or work out why a part is running warmer than you expected. This post defines the law, shows its three rearrangements, walks through a couple of real numbers, and points out the one kind of component it quietly refuses to work on.

2.0 Background Knowledge

2.1 What Ohm's Law States

Back in 1827, German physicist Georg Simon Ohm worked out the relationship that now carries his name: for a fixed resistance, the current flowing through a conductor rises in step with the voltage across it [1]. Double the voltage and you double the current. Here it is in its usual form:

$$V = IR$$

Where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω) [2], [3].

If the symbols still feel abstract, a water analogy helps. Picture voltage as the pressure pushing water through a pipe, current as how much water actually flows, and resistance as how narrow the pipe is. Turn up the pressure and more flows; pinch the pipe and less does. Same idea, just electrons instead of water.

Because it's one equation with three terms, you can rearrange it to solve for whichever quantity you're missing:

$$I = \frac{V}{R} \qquad R = \frac{V}{I}$$

2.2 Not Every Component Is "Ohmic"

Here's the catch worth knowing early. Ohm's Law only holds for resistors and other linear, or "ohmic", components: the ones where a graph of voltage against current is a straight line through zero. Diodes, LEDs, and transistors don't play by that rule. Their current doesn't rise smoothly with voltage, so dropping their numbers into V = IR gives you an answer that looks fine and is quietly wrong [4]. For those parts, reach for the curve in their datasheet instead of the formula. It's exactly why an LED needs a current-limiting resistor rather than Ohm's Law alone setting its current, which is something you can try for yourself further down.

3.0 At a Glance

Ohm's Law links three quantities. Any one of them can be found from the other two:

4.0 Formula in Action

Numbers make it click. Here are two, one solving for current and one for resistance.

Example 1: a 12 V supply is connected across a 4 Ω resistor. What's the current?

$$I = \frac{V}{R} = \frac{12\text{ V}}{4\ \Omega} = 3\text{ A}$$

Example 2: a circuit draws 0.5 A from a 9 V battery. What's the resistance?

$$R = \frac{V}{I} = \frac{9\text{ V}}{0.5\text{ A}} = 18\ \Omega$$

5.0 Common Mistakes When Applying Ohm's Law

Most slip-ups with Ohm's Law come down to units and component type, not the formula itself. The usual suspects:

• Mixing unit prefixes, like plugging milliamps (mA) or kilohms (kΩ) straight in instead of converting to amps and ohms first. The formula doesn't know about prefixes, so a stray "m" or "k" throws the answer out by a factor of a thousand.
• Applying V = IR to a non-ohmic component, such as an LED or diode, where the formula doesn't hold across its operating range.
• Forgetting real-world tolerances. A resistor labelled 220 Ω might actually measure anywhere from 210 to 230 Ω depending on its tolerance band, so your calculated and measured values won't line up perfectly.
• In a multi-component circuit, using the total supply voltage instead of the voltage drop across the one component you're actually analysing.

6.0 Project Ideas to Try Next

A few ways to put Ohm's Law to work on the bench:

• Build a simple voltage divider from two resistors and measure the voltage across each with a multimeter to confirm it matches the calculation. If you want a refresher first, what a resistor does and how voltage works both set it up nicely. It also pairs with the upcoming Voltage Divider Formula post.
• Wire an LED through a current-limiting resistor, measure the current with a multimeter, and check it against V = IR using the resistor's labelled value. Our How to Blink an LED Using Arduino and How to Fade an LED Using Arduino builds use exactly this setup, so they're a good place to see it in action.
• Swap a single resistor for two in series, then two in parallel, and recalculate the current each time to watch how the total resistance changes the result.

7.0 Covered in This Tutorial

This post covered:

• What Ohm's Law states, and its three rearrangements: V = IR, I = V/R, and R = V/I.
• Why it only applies to ohmic (linear) components, not diodes, LEDs, or transistors.
• Two worked examples, solving for current and for resistance.
• The most common mistakes when applying the formula in practice.
• Related reading: How Voltage Works and What Is a Resistor.

8.0 Conclusion

Ohm's Law is the starting point for reasoning about almost any simple circuit: hand it any two of voltage, current, or resistance, and it gives you the third. Keep it to linear, ohmic components, watch your units, and it'll get you a reliable first-pass answer every time. From here, the voltage divider and power formulas build directly on this same relationship, so the effort you put in now keeps paying off.

9.0 References

[1] G. S. Ohm, Die galvanische Kette, mathematisch bearbeitet. Berlin, Germany: T. H. Riemann, 1827.

[2] R. L. Boylestad, Introductory Circuit Analysis, 13th ed. Boston, MA, USA: Pearson, 2016.

[3] "Ohm's Law," HyperPhysics, Georgia State Univ. Accessed: Jun. 22, 2026. [Online]. Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html

[4] "Ohm's Law," All About Circuits, Direct Current, vol. I, ch. 2. Accessed: Jun. 22, 2026. [Online]. Available: https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/ohms-law/