Ohm's Law: What Is It & Why Is It Important?

Electrical circuits are ubiquitous in our day-to-day lives. From the complex integrated circuits that control the device you're reading this article on to the wiring that allows you to switch a light bulb in your house on and off, your entire life would be radically different if you weren't surrounded by circuits everywhere you go.

But most people don't really learn the nitty gritty of how circuits work and the fairly simple equations – like Ohm's law – that explain the relationships between key concepts like electrical resistance, voltage and electric current. However, delving a little deeper into the physics of electronics can give you a much deeper insight into the core rules underpinning most modern technology.

Ohm's law is one of the most important equations when it comes to understanding electric circuits, but if you're going to understand it, you'll need a good grasp of the basic concepts it links: ​voltage​, ​current​ and ​resistance​. Ohm's law is simply the equation that describes the relationship between these three quantities for most conductors.

Voltage is the most commonly used term for the electric potential difference between two points, and it provides the "push" that allows electric charge to move around a conducting loop.

Electrical potential is a form of potential energy, like gravitational potential energy, and it's defined as the electric potential energy per unit charge. The SI unit for voltage is the volt (V), and 1 V = 1 J/C, or one joule of energy per coulomb of charge. It's sometimes also called ​electromotive force​ or EMF.

Electrical current is the rate of flow of electrical charge past a given point in a circuit, which has the SI unit of the ampere (A), where 1 A = 1 C/s (one coulomb of charge per second). It comes in the form of direct current (DC) and alternating current (AC), and although DC is simpler, AC circuits are used to supply power to most households around the world because it's easier and safer to transmit over long distances.

The final concept you'll need to understand before tackling Ohm's law is resistance, which is a measure of the opposition to current flow in a circuit. The SI unit for resistance is the ohm (which uses the Greek letter omega, Ω), where 1 Ω = 1 V/A.

The German physicist Georg Ohm described the relationship between voltage, current and resistance in his eponymous equation. The Ohm's law formula is:

\(V=IR\)

where ​V​ is the voltage or potential difference, ​I​ is the amount of current and resistance ​R​ is the final quantity.

The equation can be rearranged in a simple way to produce a formula for calculating current based on voltage and resistance, or resistance based on the current and voltage. If you're not comfortable rearranging equations, you can look up an Ohm's law triangle (see Resources), but it's quite straightforward for anybody familiar with the basic rules of algebra.

The key points that the Ohm's law equation shows are that voltage is directly proportional to electric current (so the higher the voltage, the higher the current), and that current is inversely proportional to resistance (so the higher the resistance, the lower the current).

You can use the water flow analogy to remember the key points, which is based on a pipe with one end at the top of a hill and one end at the bottom. The voltage is like the height of the hill (a steeper, taller hill means more voltage), the current flow is like the flow of water (water flows faster down a steeper hill) and resistance is like the friction between the sides of the pipe and the water (a thinner pipe creates more friction and reduces the speed of the water flow, like a higher resistance does for electric current flow).

Ohm's law is vitally important to describing electric circuits because it relates the voltage to the current, with the resistance value moderating the relationship between the two. Because of this, you can use Ohm's law to control the amount of current in a circuit, adding resistors to reduce the current flow and taking them away to increase the amount of current.

It can also be extended to describe electrical power (the rate of energy flow per second), because power P = IV, and so you can use it to ensure your circuit provides enough energy to, say, a 60-watt appliance.

For physics students, the most important thing about Ohm's law is that it allows you to analyze circuit diagrams, especially when you combine it with Kirchhoff's laws, which follow on from it.

Kirchhoff's voltage law states that the voltage drop around any closed loop in a circuit is always equal to zero, and the current law states that the amount of current flowing into a junction or node in a circuit is equal to the amount flowing out of it. You can use Ohm's law with the voltage law in particular to calculate the voltage drop across any component of a circuit, which is a common problem posed in electronics classes.

You can use Ohm's law to find any unknown quantity of the three, provided you know the other two quantities for the electrical circuit in question. Working through some basic examples shows you how this is done.

First, imagine you have a 9-volt battery hooked up to a circuit with a total resistance of 18 Ω. How much current flows when you connect the circuit? By rearranging Ohm's law (or using a triangle), you can find:

\(\begin{aligned}
I &= \frac{V}{R} \
&= \frac{9 \text{ V}}{18 \text{ Ω}} \
&= 0.5 \text{ A}
\end{aligned}\)

So 0.5 amps of current flows around the circuit. Now imagine that this is the perfect amount of current for a component you want to power, but you only have a 12-V battery. How much resistance should you add to make sure the component gets the optimal amount of current? Again, you can rearrange Ohm's law and solve it to find the answer:

\(\begin{aligned}
R &= \frac{V}{I} \
&= \frac{12 \text{ V}}{0.5 \text{ A}} \
&= 24 \text{ Ω}
\end{aligned}\)

So you'd need a 24-Ω resistor to complete your circuit. Finally, what is the voltage drop across a 5-Ω resistor in a circuit with 2 A of current flowing through it? This time, the standard V = IR form of the law works just fine:

\(\begin{aligned}
V&=IR \
&= 2 \text{ A} × 5 \text{ Ω} \
&= 10 \text{ V}
\end{aligned}\)

You can use Ohm's law in a huge range of situations, but there are limitations to its validity – it isn't a truly fundamental law of physics. The law describes a linear relationship between voltage and current, but this relationship only holds if the resistor or resistive circuit element you're working with has a constant resistance under different voltage ​V​ and current ​I​ values.

Materials that obey this rule are called ohmic resistors, and although most physics problems will involve ohmic resistors, you'll be familiar with many non-ohmic resistors from your day-to-day life.

A light bulb is a perfect example of a non-ohmic resistor. When you make a graph of ​V​ vs. ​I​ for ohmic resistors, it shows a completely straight-line relationship, but if you do this for something like a light bulb, the situation changes. As the filament in the bulb heats up, the resistance of the bulb ​increases​, which means the graph becomes a curve rather than a straight line, and Ohm's law doesn't apply.