What is Ohms Law – formula, equation & triangle

Ohm's Law is one of the most fundamental of laws for electrical theory. The Ohms Law formula links voltage and current to the properties of the conductor in a circuit.

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Ohm's Law is one of the most fundamental and important laws governing electrical and electronic circuits. It relates relates current, voltage and resistance for a linear device, such that if two are know, the third can be calculated.

With current, voltage and resistance being three of the major circuit quantities, this means that Ohm's Law is also immensely important.

Ohm's Law is used within all branches of electrical and electronic science. It is used for calculating the value of resistors required in circuits, and it can also be used for determining the current flowing in a circuit where the voltage can be measured easily across a known resistor, but more than this, Ohm's Law is used in a vast number of calculations in all forms of electrical and electronic circuit- in fact anywhere that current flows.

Ohm's Law - circuit, concept and triangle

Ohm's Law discovery

There is a mathematical relationship which links current, voltage and resistance. A German scientist named Georg Ohm performed many experiments in an effort to show a link between the three. In the days when he was performing his experiments there were no meters as we know them today.

Only after considerable effort and at the second attempt did he manage to devise what we know today as Ohm's Law.

Note on Georg Ohm:

Born in Erlangen, about 50 miles north of Munich in 1879, Georg Ohm went on to become one of the people who investigated much about the new science associated with electricity, discovering the relationship between voltage and current in a conductor - this law is now named Ohm's Law, honouring the work he did.

Read more about Georg Ohm.

What exactly is Ohm's Law?

Ohm's Law describes the way current flows through a material when different levels of voltage are applied. Some materials like electrical wires present little resistance to the current flow and this type of material is called a conductor. Hence if this conductor is placed directly across a battery for example, a lot of current would flow.

In other instances another material may impede the flow of current, but still allow some though. In electrical circuits, these components are often called resistors. Yet other materials let virtually no current though and these materials are called insulators.

Ohm looked at the way current flowed in various materials and he was able to develop his law which we now call Ohm's Law.

To gain a first idea of what is happening it is possible to liken the electrical situation to that of water flow in a pipe. The voltage is represented by the water pressure the pipe, the current is represented by the amount of water flowing through the pipe, and finally the resistance is the equivalent of the size of the pipe.

It can be imagined that the wider the pipe, the more water will flow. The reason for this is that it is easier for more water to flow through a wider pipe than a narrower one - the narrower one presents more resistance to the water flow. Also if there is more pressure into e pipe, then for the same pipe, more water will flow.

Ohm determined that for normal materials, doubling the voltage doubled the current flow for a given component. Different materials or the same materials with different shapes will present different levels of resistance to the flow of current.

Ohm's Law definition

Ohm's Law states that the current flowing in a circuit is directly proportional to the applied potential difference and inversely proportional to the resistance in the circuit.

In other words by doubling the voltage across a circuit the current will also double. However if the resistance is doubled the current will fall by half.

In this mathematical relationship the unit of resistance is measured in Ohms.

Simple illustration of Ohm's Law in a  circuit

Ohm's Law formula

The Ohm's Law formula or equation is very straightforward.

Ohm's law can be expressed in a mathematical form:

V = I R
    V = voltage expressed in Volts
    I = current expressed in Amps
    R = resistance expressed in Ohms

The formula can be manipulated so that if any two quantities are known the third can be calculated.

I = V R
R = V I

Ohm's law triangle

To help remember the formula it is possible to use a triangle with one side horizontal and the peak at the top like a pyramid. This is sometimes known as the Ohm's law triangle.

In the top corner of the Ohms law triangle is the letter V, in the left hand corner, the letter I, and in the right hand bottom corner, R.

Ohm's Law triangle showing the voltage, current and resistance

To use the triangle cover up the unknown quantity and then and then calculate it from the other two. If they are in line they are multiplied, but if one is on top of the other then they should be divided. In other words if current has to be calculated the voltage is divided by the resistance i.e. V/R and so forth.

Ohm's Law triangle split out for different equations

If the voltage has to be calculated then it is found by multiplying the current by the resistance i.e. I x R.

Ohms Law calculation example

If a voltage of 10 volts is placed across a 500 ohm resistor determine the amount of current that will flow.

Simple Ohm's Law example calculation

Looking at the Ohms Law triangle the current is the unknown leaving the voltage and resistance as the known values.

Using the Ohms Law triangle for a calculation

In this way the current is found by dividing the voltage by the resistance.

I   =   V R   = 10 500 = 0.02 A = 20 m A

Example 2
In a similar way it is possible to use Ohm's Law to find the resistance if the current and voltage are known. Take, for example, a voltage of 10 volts, and a current 0.1A. Using the Ohm's Law triangle, it can be seen that:

R = V I = 10 0.1 = 100 Ω

Example 3
Finally, the other combination is that is the resistance and current are known, then it is possible to calculate the voltage expected across the resistance. Take the example of a distance of 250 Ω which has a current of 0.1 A flowing through it, then the voltage can be calculated as below:

V = I   R = 0.1 × 250 = 25   volts

Linear graph

It can be seen that if the voltage and current were plotted for a fixed resistor or a length of wire, etc, there would be a linear curve.

Plot of voltage and current for a linear resistance
Plot of voltage and current for a linear resistance

It can be seen that doubling the voltage doubles the current that passes through the particular circuit element.

On the graph, there are two lines, one for a higher resistance - this one requires more voltage to be applied for a given current flowing. Accordingly this must have a higher resistance. Conversely the curve for the lower resistance shows a component that requires a lower voltage to be applied for a given current.

Non-linear components

Ohm’s law in its basic form where a doubling in voltage results in a doubling in current applies to linear components like ordinary resistors. Some components like diodes have non-linear curves where the resistance is affected by the applied voltage.

Ohm’s Law is one of the most basic concepts within electrical and electronic engineering. The concept of an item having a certain resistance which determines the amount of current that flows through it for a certain voltage is key to the operation virtually all circuits.

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