Are you curious about whether your car battery is dying? How much power from the wall outlet is going to your coffee maker? Or maybe you’re struggling with a project in electricity and need a refresher! Whatever it may be, this blog post will teach you the basics of Ohm’s Law.
In the study of electricity, the relationship between different electrical quantities is pivotal. These electrical quantities include current, voltage, resistance, capacitance, inductance, etc. We will look at the relationship between resistance, Voltage, and current in an electric setup. Ohm’s law was formulated in 1827 by Georg Simon Ohm, a physicist, who studied how electromotive force, resistance, and current relates to an electric circuit. His study led to the formulation and publication of Ohm’s law, which greatly relied on inspiration from previous scientists who had analyzed resistance and other related theories. The voltage source used was a thermocouple, whose junction temperature is proportional to the Voltage across its terminals during this formulation. We can start by first defining Ohm’s law and later studying different principles about it, and later digging deeper into its relationship with other formulations, its applications, and also its limitations if there exists.
What is Ohm’s law?
Ohm’s law definition illustrates the connection between the potential difference, electric current, and resistance. According to Ohm’s law, the magnitude of stable current flowing through an electric material is directly proportional or relative to the potential difference (Voltage) across its endpoints. In other words, Ohm’s law states that the potential difference across the endpoints of an electric conductive material is directly proportional to the amount of electric current that flows through it and inversely proportional to its total resistance, as long as its temperature and also physical conditions are kept constant. However, in some materials, such as the filament of a bulb, its temperature increases with an increase in the current through them, and hence Ohm’s law may not be relevant.
Analysis of Ohm’s law using the water pipe analogy
People have come up with certain comparisons with the aim of achieving clarity for Ohm’s law. For example, the idea of water flowing through pipes can explain the relations of Ohm’s law in an electric circuit. In this case, we take the Voltage to be the pressure of the water, the amount of water passing through the pipe represents the total current in the circuit, and the pipe size represents the resistance. In a big pipe (lower resistance), applying more pressure(Voltage) forces more water(current) to flow through the pipe. Therefore, when the resistance is kept constant, an increase in the Voltage across the ends of the material results in a corresponding increase in the amount flowing through the material. Clearly, this illustrates that the potential difference across the endpoints of the material is directly proportional to the amount of electric current flowing through the material.
What is the mathematical expression of Ohm’s law?
Mathematically, we denote Ohm’s law as V=IR,
where V represents the Voltage across the endpoints of the material measured in units of volts(V), I represents the electric current passing through the material measured in Amperes(A), and R represents the resistance of the material measured in Ohms(Ω).
From the equation V=IR, the current(I) can be expressed in terms of potential difference(V) and resistance(R) as follows:
We can also express the resistance of the material, (R) in terms of potential difference, (V) across the material, and the electric current(I) through the material as follows:
Magic triangle for the Ohm’s law formula
We represent the equations for Ohm’s law in a simple triangle displaying the three variables, potential difference(V), current(I), and resistance(R), as shown in the figure below:
With this triangle, given two variables, the third one can be easily calculated by covering the variable in question and then using the other two with the operator between them. For example, given the potential difference and the resistance in a circuit, we can find the formula for calculating the current through the circuit by covering I in the triangle and taking V and R with the operator between them. Therefore, I=V/R.
Examples of Ohm’s law problems
Example 1
A current of 4.0 A flows through an electric kettle of resistance 80.0 Ω. Find the potential difference across the electric kettle.
Solution
In this problem, I= 4.0A and R= 80.0 Ω
Using Ohm’s law formula, , we can easily substitute the given values and then solve for the potential difference(V)
V= IR
=4.0 x 80.0
=240.0 V
Example 2
A resistor of unknown resistance is connected to a DC supply of 20.0V. If a current of 5.0A runs through the resistor, calculate the resistance value of this resistor. (In this case, assume that the conducting wires used in the setup had negligible resistance)
Solution
Here, V= 20.0V
I= 5.0A
By Ohm’s law,
Making R the subject of this formula,
Therefore,
= 4.0 Ω
Example 3
A resistive light bulb with a resistance of 10.0 Ω is connected to a battery that produces an EMF of 12.0V. Calculate the amount of electric current flowing through the light bulb.
Solution
The resistance(R) and the potential difference(V) are given in this problem.
R= 10.0 Ω
V= 12.0V
Applying Ohm’s law:
To calculate the value of current passing through the light bulb, we make I the subject of the formula by dividing both the right-hand side and the left-hand side of the equation by R.
Therefore, the equation becomes:
=1.2A
Graphical representation of Ohm’s law
Graphically, We can express Ohm’s law by plotting a graph of the electrical current(I) through the material against the Voltage (V) across the material.
For instance, given the following data:
| Voltage(V) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 |
| Current(A) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 |
The graph of Voltage against the current will be a straight line with a positive gradient as shown below:
We can describe the resistance of the conductive material as the ratio of the change in the potential difference across its endpoints to the corresponding change in the electric current flowing through it.
We are verifying Ohm’s law experimentally.
Let us now look at how we can easily verify Ohm’s law experimentally.
Apparatus
- DC supply
- Connecting wires
- Ammeter
- Rheostat
- Voltmeter
- Plug key
- Resistor
Procedure
The circuit is connected as shown in the figure below:
In this experiment, the first step is closing the key K and adjusting the Rheostat to get the minimum ammeter and voltmeter reading. You then move the terminal of the Rheostat gradually to increase the electric current in the circuit and at the same time record the values of the current flowing through the circuit and the corresponding potential difference across the resistance wire. The collection of different data values of Voltage and electric current therefore result. The ratio V/I is then calculated and recorded. As you’ll notice, this ratio gives almost similar values for each data set. Since this ratio gives a constant, it gets the representation R, which stands for the resistance of the electric circuit. Therefore, V/I=R.
Using Ohm’s law to calculate electric power
We can define electric power(P) as the rate at which electrical energy in a circuit is converted to other forms of energy, for example, heat, mechanical energy, or magnetic fields. We express electric power in units known as watt(W). By applying Ohm’s law, the electric power in a certain circuit can be easily calculated, provided the current, Voltage, and resistance values are given.
We use the following formula to determine the electric power in a given circuit:
P=VI
From Ohm’s law, V=IR. Therefore, we can express electrical power(P) as:
P=(IR)I
Therefore, on opening the brackets, the equation becomes:
P=I2R
However, the only values provided are Voltage (V) and resistance(R) in some cases. We, therefore, calculate the electric power as shown below:
P=VI
But from Ohm’s law, the current (I) can be expressed as
Substituting in the formula for electric power, P=VI
=V ()
=V2/R
The power triangle
Given the potential difference (V) and the electric current (I) values, we can easily calculate the electric power using a simple triangle known as the power triangle. We can express as shown in the figure below:
To get one of the three variables, given the other two, you cover the variable in question and take the other two with the operator between them. For instance, given the electric current and the potential difference, we can calculate the electric power by covering P in the power triangle and taking I and V with the operator between them. Therefore, P=V x I.
Examples of electric power problems
Example 1
An electric iron is connected to an EMF source of 120.0V. Calculate the electric power it consumes if the electric current through it is 6.0A.
Solution
In this problem, V= 120.0V and I= 6.0A.
Using the formula for power,
P= VI
=120.0 x 6.0
=720.0 W
Example 2
A resistor with a resistance value of 20.0Ω is connected to a DC supply producing an EMF of 12.0V. Next, calculate the total electric power in this electric circuit.
Solution
Here, V is given as 120.0V, and R is given as 20.0 Ω
Therefore, we can get the electrical power P by applying the formula:
P= V2/R
=120.02/ 20.0
=720.0W
Example 3
In a resistive electric circuit, the current flowing through the circuit was measured as 10.0A. If the total resistance in the circuit was 30.0 Ω, calculate the total electric power dissipated in this electric circuit.
Solution
Given that the current (I) = 10.0A, and the total resistance (R) = 30.0 Ω, we can calculate the electric power using the formula:
P = I2R
= 10.02 x 30.0
= 100.0 x 30.0 = 3000.0 W
Pie chart for Ohm’s law
An Ohm’s law pie chart is a simple representation that combines various parameters related to current, electromotive force, power, and resistance. For example, we represent the pie chart as shown in the figure below:
The matrix table for Ohm’s law
We can also condense all the equations for Ohm’s law into a simple matrix table that makes it easier to reference when calculating different values.
| Known | Resistance (R) | Current (I) | Voltage(V) | Power (P) |
| Resistance andcurrent | . . . . . . . . . . . . . . | . . . . . . . . . . . . . . | V = I x R | P = I2 x R |
| Current and voltage | R = V / I | . . . . . . . . . . . . . . | . . . . . . . . . . . . . . | P = V x I |
| Power and current | R = P / I2 | . . . . . . . . . . . . . . | V = P / I | . . . . . . . . . . . . . . |
| Resistance and Voltage | . . . . . . . . . . . . . . | I = V / R | . . . . . . . . . . . . . . | P = V2 / R |
| Resistance and power | . . . . . . . . . . . . . . | I = √ (P / R) | V = √ (Z x R) | . . . . . . . . . . . . . . |
| Voltage and power | R = V2 / P | I = P / V | . . . . . . . . . . . . . . | . . . . . . . . . . . . . . |
Ohm’s law and Newton’s 2nd law of motion
While Ohm’s law is about dealing with the relationship between resistance (R), Voltage (V), and current (I) in electric circuits, Newton’s 2nd law focuses on the connection between force (F), acceleration (a), and mass(m). However, the equations of the two relations can base on the same principle governing the force acting on different particles and matter entirely. The relationship between mechanical power and electric power is clear, since we often use electric power to generate power for running mechanical systems, for example, in electric lifts and electric vehicles. Similarly, we use mechanical systems in the generation of electrical power. Due to this relation, new units have been in formulation to combine the two. In mechanical systems, for example, we measure the motion of a particle as velocity in units of meters per second (m / s).
The improved formula
In contrast, we measure that of an electron in an electric system as current, in units of amperes (A). If we view the charge as a wave, its amplitude is simply a displacement. In this case, the units of Coulombs (C), therefore, can be transformed into units of displacement, meters (m) and hence aligning the units, and the relationship is therefore clear. Destructive and constructive interference are properties of waves that allow charges to combine or neutralize each other based on the nature of the interference. Units can therefore replace the units Coulomb (C) for distance, meters (m), the charge (e). The units, therefore, will be . Therefore, we can replace the units of all the Ohm’s law’s components as shown below:
We measure Power in watts in an electrical system, P = VI. In mechanical systems, we measure power in watts. Therefore, we can express the units of power as follows:
The table below summarizes the relationship between electrical and mechanical systems and their corresponding corrected units:
| Electrical system | Mechanical system | Corrected Units | ||
| Power (P) | watts | = | watts | |
| Voltage (V | volts | = | newtons | |
| Current (I) | amperes | = | velocity | |
| Resistance (R) | ohms | = | mass/time |
In the table above, the current has been converted to a velocity, Voltage to a force with its units in newtons (N). The power has retained its units for both electrical and mechanical systems.
Non – Ohmic and Ohmic Conductors
From Ohm’s law, a straight-line graph would result when you plot current and Voltage on an axis. Increasing the potential difference across a conductive material increases the electric current flowing through it. However, some conductors have higher resistance and therefore require the application of more Voltage for the production of a certain current. On the other hand, other conductors require the application of lower Voltage for a certain amount of current to be produced. Conductors whose graphs are linear and follow Ohm’s law are Ohmic conductors. However, some electric components may portray different current/voltage characteristics, and their graphs may not be linear plots. Such conductors are said to be non–Ohmic conductors. The figure below shows the shapes of line graphs for both Ohmic and non–Ohmic conductors.
For example, the copper connecting wires used for electrical components are good examples of an Ohmic conductor. This is because its temperature remains constant under normal conditions since the heat dissipated is very low. As a result, the potential difference between the wire terminals is low, resulting in lower resistance. However, the wire still follows Ohm’s law. Resistors used in electronic components are also a good example of ohmic conductors. They consist of an ohmic leaded metal film. Ohmic resistors are used in electronic components to provide fixed resistance within the circuit and hence to set voltages and limit the amount of current through these components.
Is there a considerable example?
A good example of a non–ohmic conductor is the incandescent light bulb. These bulbs convert electrical energy to light energy efficiently. However, they generate a lot of heat as they are heated to high temperatures, become white-hot, and produce light. An increase in temperature leads to increased resistance of the filament. As a result, the current through the filament is reduced, setting the lamp to a normal operation.
A semiconductor diode is also an example of a non–ohmic conductor. It consists of a p – n junction and allows the current to flow through it in only one direction. It has approximately no forward resistance and substantially large resistance in the opposite (reverse) direction. Most semiconductor devices are non–ohmic conductors. For example, varistors used for protecting line transients or mains power have a high resistance that falls only on exceeding a certain set voltage, absorbing the transient and protecting the powered units.
Applications of Ohm’s law
- Ohm’s law is normally applicable in controlling the speed of fans, which you can achieve by changing the regulator’s position from the end to the starting point. In addition, one can achieve the current flowing through the fan by using the regulator to control the resistance. We can measure the power, resistance, and current flowing through the fan by applying Ohm’s law.
- Circuit breakers and fuses are in a series connection with electrical appliances for circuit protection. Therefore, we can determine the electric current flowing through the fuse by applying Ohm’s law.
- In electrical appliances such as electric irons and kettles, many resistors restrict the amount of electric current flowing through them and, in the process, provide the required amount of heat. The suitable size of the resistors used is determined using Ohm’s law.
- Ohm’s law is applicable in electrical heaters, which have metallic coils with high resistance to determine the power consumed by the heaters during their operation.
Limitations of Ohm’s law
- For non-metallic conductors such as graphite, we cannot apply Ohm’s law since it is only workable for metallic conductors.
- Unilateral electrical components such as transistors and diodes only allow current to flow through them in one direction. Therefore, it is impossible to apply Ohm’s law to such elements.
- In diodes, for example, if the magnitude of the Voltage is maintained, but you reverse its direction, the magnitude of the current produced will be different from that produced in the opposite direction. Ohm’s law will therefore not hold in both directions since the relationship between the current (I) and the Voltage (V) depends on the nature of V. That is, it depends on whether the sign of V is positive or negative.
- Ohm’s law cannot be applied for electrical circuits with non-linear electrical components such as resistors, capacitors, etc., since the current through them and the potential difference across them may not be constant throughout. For non-linear elements such as thyristors and electric arc, the applied Voltage is not proportional to the amount of current through them. Therefore, the resistance will change with changes in the values of current and potential difference, and therefore, the application of Ohm’s law will be difficult.
Conclusion
As we have seen in this article, Ohm’s law is a basic concept in the study and application of electricity, one of the branches in Physics. We often interact with electricity in our day-to-day activities while working with different electrical appliances. Therefore, it is very important to understand the basic principles of the functioning of these appliances. This article has looked at Ohm’s law, its mathematical and graphical expression, and how it can be verified experimentally. We have also addressed other analogies explaining Ohm’s law like the relationship of Ohm’s law and Newton’s 2ndlaw of motion. Therefore, the relationship leads to new units that interconnect mechanical and electrical systems. We have also looked at Ohm’s pie chart, Ohm’s triangle, and Ohm’s law matrix as other ways to represent Ohm’s law.
In calculating electrical power, we can employ Ohm’s law to simplify the operations. We have seen the different areas where we can apply Ohm’s law in our daily activities and highlighted its limitations.
It is obvious that Ohm’s Law is incredibly important and should be a part of every engineer’s common knowledge. Hopefully, you now have a better understanding of Ohm’s Law and can apply it to your own applications.
