Ohm’s law was formulated in 1827 by the German physicist Georg Simon Ohm based on experiments he performed on simple electrical circuits containing various lengths of wire.
Ohm’s law is one of the most fundamental and important principles of electrical circuits.
Ohm’s law states that the voltage across two points in an electric circuit is directly proportional to the current passing between those two points. The constant of proportionality is equal to the resistance.
The formula for Ohm’s law is:
Here, V is the voltage across a conductor, I is the current passing through the conductor, and R is the electrical resistance of the conductor. The resistance in Ohm’s law is always equal to a constant value and can be calculated by taking a series of voltage and current measurements over a suitable range of values before plotting the data on a straight-line graph and calculating its gradient.
Before continuing with our explanation of Ohm’s law, we should review some basic concepts around electric circuits.
Ohm's Law: Electric circuits
An electric circuit is a set of electrical components connected by conducting wires through which an electric current can pass. An electric current consists of moving electrons that flow around the wire under the influence of an applied voltage. In order for electric components to allow the flow of electric charge, they must be made of electrically conductive materials. A conductor is a material or electrical component that facilitates the flow of charge (electric current) in one or more directions. We say that such materials are good conductors of electricity.
Example of an electric circuit, adapted from image by: MikeRun CC BY-SA 4.0
Metals are good conductors of electricity, which is why we create electric circuits, such as the ones used in everyday electronics, out of copper, which is highly conductive.
When studying electric circuits, we often make the distinction between Ohmic conductors and non-Ohmic conductors.
An Ohmic conductor is a conductor that obeys Ohm’s law.
The voltage vs current graph of an Ohmic conductor has a linear relationship, which is not the case for non-Ohmic conductors.
Graph of voltage vs current for an Ohmic material and for a Non-Ohmic material, Iñaki Caparros-Vaia Originals
A non-Ohmic conductor does not obey Ohm’s law. The relationship between voltage and current for a non-Ohmic conductor is non-linear.
The behaviour of non-Ohmic conductors is not necessarily the same as that shown in the figure above. The important feature is that there is a non-linear relationship between current and voltage, which means that the graph of voltage vs current is not a straight line. Some examples of non-Ohmic conductors are bulb filaments or some semiconductors such as transistors or diodes.
Some materials don’t conduct electricity very well. We refer to such materials or electrical components made of such materials as insulators.
Insulators can be used to slow or halt the flow of charge and boast a variety of real-world applications, such as the plastic covering of electrical wires that prevents us from receiving an electric shock.
Ohm's Law: Voltage
Voltage is also known as potential difference. The potential difference across two points in a conductor is equal to the difference in electric potential between two points. The potential difference in an electric circuit is generated by cells or batteries. In standard units, we express potential difference/voltage in volts (V).
In electrical circuits, voltage is generated by a cell or a battery, which has a positive terminal with a higher potential and a negative terminal with a lower potential.
Ohm's Law: Current
Current is the rate of flow of electric charge. The device that we use to measure current in an electric circuit is called an ammeter. The standard unit for electrical current is the Ampere (A).
Ohm's Law: Resistance
Resistance is a measurement of the degree to which conductors resist the flow of electricity. The standard unit for resistance is an Ohm (Ω). The resistance of an electric conductor increases with length and decreases with thickness. The resistance also depends on the type of material it is made from.
Aluminium wire has a higher resistance than copper wire of the same length and cross-sectional area, which means that copper is a better conductor of electricity than aluminium. But an aluminium wire has a smaller resistance than a copper wire four times its length.
To increase the electrical resistance of an electric circuit, we might want to add a component called a resistor. A fixed resistor obeys Ohm’s law, and different fixed resistors have different fixed resistances for different uses.
Examples of resistors that offer different resistance in electric circuits.
The derivation of Ohm’s law
There is no exact derivation for the formula of Ohm’s law. As mentioned earlier, the law was stated in 1827 by Georg Simon Ohm, but it is an empirical law, which means that it was originally based on observations rather than derived from first principles. Ohm discovered the law by observing the behaviour of Ohmic conductors whilst applying a current to them. Based on the data obtained, Ohm stated that there was a linear relationship between the current and the intensity, but he did not derive the law theoretically.
The formula for Ohm’s law revisited
Now that we have uncovered what each term in Ohm’s law means, let’s remind ourselves of the formula:
Or, to put this into words:
We can see from the equation that there is a direct relationship between the voltage and the intensity of the current. We say that the voltage across a conductor is directly proportional to the current passing through it. This means that if we increase the current passing through a conductor by a certain factor, the voltage will increase by the same factor and vice versa. For example, if we double the potential difference across a wire, the current passing through it will also double.
We can rearrange the formula for Ohm’s law to make the resistance or the current the subject of the formula. If we know the values of any two variables in Ohm’s law, we can calculate the value of the remaining missing variable.For example, if we know the current passing through a component in an electric circuit and we also know the potential difference between two sides of the component, we can calculate the resistance of the conductor with the following formula:
This is still Ohm’s law, just rearranged to make R the subject of the formula. Likewise, if we know the potential difference across a component and its resistance, we can calculate the current I passing through it:
We can use the following diagram to remind ourselves of how to calculate each of the variables in Ohm’s law when we know the values of the other two.
Ohm's law triangle with voltage (V), current (I), and resistance (R), Iñáki Caparros-Vaia Originals
This triangle is called the Ohm’s law triangle. To remind ourselves of how to calculate each of V, I, and R, we set up the triangle, with V in the top segment and I and R in the bottom segments. To calculate the value of either of the variables at the bottom of the triangle, we simply divide the value of V by the value of the other remaining variable in the bottom part of the triangle. V is simply calculated by multiplying the values of the two variables in the bottom segment of the triangle, namely I and R.
If you struggle to rearrange equations, you may prefer to calculate V, I, and R using the Ohm’s law triangle. Just remember to draw a triangle and separate it into three parts, the part at the top containing V and the two bottom segments containing I and R.
A 9 V battery produces a current of 3 A in a wire. What is the resistance of the wire?
To solve this problem, we use Ohm’s law. Using our knowledge of rearranging equations or the Ohm’s law triangle, we find that the formula to compute the resistance is:
To find either of the two variables in the bottom level of the Ohm’s law triangle, we divide the voltage by the other variable in the bottom level. In this case, we divide V by I to find R.
Therefore, the resistance of the wire in this example is:
Determine the voltage of an electric circuit with a current of 0.5 A and a resistance of 20 Ω.
In this case, we need to use the first form of Ohm’s law. We find the formula of Ohm’s law for the voltage using the Ohm’s law triangle:
Now, we can introduce the data for the electric circuit provided in the question by substituting 0.5 A for the current and 20 Ω for the resistance:
Given the following electric circuit, calculate the current passing through it once the switch is closed.
Electric circuit with a voltage V= 30 V and resistance of R= 10 Ω, Iñaki Caparros-Vaia Originals
As we can see in the figure above, the electric circuit has a potential difference of 30 V across its terminals, and the resistor has a resistance of 10 Ω. We have to rearrange the original form of the Ohm’s law formula. If we take a look at the Ohm’s law triangle, we can rearrange the formula to calculate the current:
Using the values of the variables provided in the figure, we can calculate the current as follows:
Ohm’s Law - Key takeaways
- Ohm’s law states that the voltage or potential difference V across two points in an electric circuit is proportional to the current passing through it, and the constant of proportionality is the resistance.
- The general expression for Ohm’s law is V = IR.
- An electric circuit is a set of electrical components connected with wires through which an electric charge flows. It consists of elements made of conductive materials that allow the electric charges to move along them. Materials that do not conduct electricity well are called insulators.
- Voltage is the difference in electric potential between two points. The standard unit of voltage is the volt (V).
- Current is the rate of flow of electric charge. The standard unit of current is the ampere (A).
- Resistance is the property of a conductor that resists the flow of electric charge. The standard unit for resistance is the Ohm (Ω).
- Ohm’s law can be used to calculate voltage, resistance, and the current of electric conductors, provided the other two variables are known. One way to remember the Ohm’s law formula is the Ohm’s law triangle.
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