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Ohm’s law exists as the fundamental law behind the other formulas. Understanding this law will greatly help us in understanding how an electrical circuit works. For this purpose we will be accompanied by a resistor, the simplest passive element.

What is Ohm’s law actually?

How to use it?

At first, we will get confused by its name. Why does it have to be Ohm’s law? All formulas are named after the name of the inventor.

This law exists to get a measurement of ‘Electrical Resistance’. Not only that, this law will lead to the “Electrical Impedance” measurement.

For an AC circuit you will replace the resistance with impedance. If we have the values of two from three elements then we can find the third value element easily.

Why is Ohm’s law very important for us to learn? Because its elements in its equation are the major variables. You will find voltage, current, and resistance (or impedance) in every electric circuit you find or use.

Not only that, Ohm’s law is used for the advanced laws, theorems, and calculations. Ohm’s law is used in every aspect of electrical and electronic circuits, where the electric current is flowing.

In this post, we will learn all about Ohm’s law. I will provide the circuit analysis, its application, and an easier method to use. What is Ohm’s law formula is our top priority here.

Not only its equation, here you will find an easier illustration to remember it very well.

Before learning Ohm’s law, it is wise for you to read what an electric circuit is first.

Ohm’s Law First Discovery

The Ohm’s law formula was not discovered from nothing. This Ohm’s law forms a relationship between voltage, current, and resistance in an electrical circuit. Later we will read about Ohm’s law definition.

If we want to give credit to Ohm’s law, it should be for Georg Ohm. He is a German scientist who performed numerous experiments in order to find the relationship between voltage, current, and resistance in a single equation. This law is the ‘father’ of all electrical laws and theorems.

A German physicist, Georg Ohm is the one who invented this law in 1827.

What is Ohm’s Law

The theory of ohm’s law experiment is the relationship between voltage, current, and resistance. It states that the voltage varies as the current varies (and vice versa), given that all other variables remain the same.

When asked what is the Ohm’s law definition?

Ohm’s law states that the current is proportional to voltage but inversely proportional to resistance

Or

Ohm’s law states that voltage across a resistor is proportional to the current flowing through it.

What makes the voltage and current vary in the circuit? It is related to the resistance in that circuit.

Ohm’s Law Theory

After we have known  that voltage, current, and resistance are the pillars of Ohm’s law, we will try to understand it deeper and better.

How does Ohm’s law theory work?

Ohm’s law theory illustrates how the current is flowing through any material when a voltage is applied. One thing to remember is the difference between low resistance and high resistance. An electrical wire or any conductor has low resistance, it means the current will flow easily. Otherwise, if the resistance is high then the current will have a hard time to flow.

To make it simpler, because the amount of current flowing in the circuit is determined by the voltage divided by the resistance, more resistance means less current and vice versa.

Normally any conductor has very small resistance thus we can ignore it in our calculation. On the other hand, any material which is not able to deliver electric current is an insulator.

Resistance, measured in ohms (Ω), is determined by the material. Different materials with different sizes provide different resistance from one another.

Ohm’s law is represented by a linear relationship graph between voltage (V) and current (I) in an electric circuit. We can imagine the Ohm’s law using the water pipe illustration:

  • The water pipe is the resistance (R) in the circuit, measured in ohms (Ω).
  • The water is the electrical current (I) flows in the circuit, measured in amperes (A).
  • The height difference between the water is the voltage (V) in the circuit, measured in volts (V).

The illustration goes like these:

  • If the water pipe is thin (resistance is high), it limits the water (electric current) flows in the circuit.
  • If the water pipe is wide (resistance is low), it increases the water (electric current) flowing in the circuit.
  • Every material has a unique characteristic to resist electric charge flow. Their physical ability to resist current has been known as resistance with the symbol R.

Ohm’s Law Equation

Keep in mind that both “Ohm’s Law” that measures the resistance in the circuit and “Resistance” that measures how well a resistor resists electric current, they are both represented by “R”

The resistance of a resistor is calculated from

    \begin{align*}R=\rho\frac{l}{A}\end{align*}

Where:
ρ = resistivity of the material, measured in ohm-meters.
l = length of a resistor
A = cross-sectional area

We will go no further than this because this is not what we are looking for.

Continuing what we left earlier, the Ohm’s law consists of a voltage, a current, and a resistance. This way we will use a simple electrical circuit consisting of one each of them.

Observe the Ohm’s law circuit below with a voltage source and a resistor. These two will produce electric current.

ohm's law 1

From the previous explanation, we have:

  • The voltage varies with the current (and vice versa) while all other variables remain the same.
  • Current is proportional to the voltage (and vice versa) but inversely proportional to the resistance.

From the two points above we can write the Ohm’s formula as

    \begin{align*}I=\frac{V}{R}\quad\mbox{or}\quad V=IR\quad\mbox{or}\quad R=\frac{V}{I}\end{align*}

which is the mathematical equation of Ohm’s law.

V represents voltage in the circuit, measured in volts (V) but for some people use E instead. Where E is electromotive force or voltage.

I represents current flowing in the circuit through every element (resistor in the circuit example) measured in amperes (A).

R represents resistance of the resistor measured in ohms (Ω).

We conclude that:

  • If the voltage is increased, the current will also increase.
  • If the resistance is increased, the current will reduce.

So,

The resistance R of an element denotes its ability to resist the flow of electric current, measured in ohms (Ω).

We can deduce the equation to

    \begin{align*}R=\frac{v}{i}\end{align*}

so that

    \begin{align*}1\Omega=1\mbox{V/A}\end{align*}

From the definition above we know that:

Ohm’s law states that the potential difference (voltage) between two points is proportional to the current flowing through a resistor, and also proportional to the resistance of the circuit. Summary, the Ohm’s law formula is simply V=IxR.

Ohm’s law Formula

We can find the value of voltage, current, and resistance with Ohm’s law if we have two of the three variables. For example:

Voltage calculation Ohm’s law formula

If we have the value of the resistance and the current, we will be able to find the value of the voltage with:

[V = I x R] —– Voltage (Volt) = Current (Ampere) x Resistance (Ω)

Current calculation Ohm’s law formula

[I = V / R] —– Current (Ampere) = Voltage (V) / Resistance (Ω)

Resistance calculation Ohm’s law formula

If we have the value of the voltage and the current, we will be able to find the value of the resistance with:

[R = V / I] —– Resistance (Ω) = Voltage (V) / Current (Ampere)

The value of R varies from zero to infinity. Hence, it is important to take note of two extreme possible values of R.

Zero resistance and short circuit

An element with the value R = 0 is a short circuit.

ohm's law 2

So,

    \begin{align*}v=iR=0\end{align*}

indicating that the voltage is zero but the current could be any value. In other words, the short circuit is usually assumed by a connecting wire that is the perfect conductor.

Hence.

A short circuit is a circuit element with resistance approaching zero.

Infinite resistance and open circuit

In contrast, an element with R = ∞ is an open circuit as can be below. For an open circuit,

ohm's law 3

Then,

    \begin{align*}i=\lim_{R \rightarrow \infty}\frac{v}{R}=0\end{align*}

indicating that the current is zero through the voltage could be any value.

Hence,

An open circuit is a circuit element with resistance approaching infinity.

Ohm’s Law Triangle

By knowing two of the three variables from Ohm’s law, we will easily find the questioned variable.

Hence, if we want to know the value of the current, we have to know the values of the voltage and the resistance.

Below is the well-known Ohm’s law triangle.

ohm's law 4

Just as stated above:

To calculate voltage (V)

[V = I x R] —– Voltage (Volt) = Current (Ampere) x Resistance (Ω)

To calculate current (I)

[I = V / R] —– Current (Ampere) = Voltage (V) / Resistance (Ω)

To calculate resistance (Ω)

[R = V / I] —– Resistance (Ω) = Voltage (V) / Current (Ampere)

ohm's law 5

This Ohm’s law will be used a lot including the Kirchhoff’s Laws.

Ohm’s Law Pie Chart

Ohm’s Law shows the relationship between Voltage (V or E), Current (I), and Resistance (R).

Thus, we add the Joule’s law to perfect the ohms law wheel. Joule’s law states that power is the multiplication of voltage and current.

As a result, the combination of these two will provide us with 12 formulas with 2 known variables.

Therefore, we get the ohm’s law wheel below along with their measurement units.

ohm's law 6

Limitation of Ohm’s Law

Even this is the most basic circuit analysis, it still has some limitations such as:

  • Can’t be used for a unilateral electrical network (diode transistor, etc) that doesn’t have linear voltage-current relationship.
  • Can’t be implemented for a nonlinear circuit.

Ohm’s Law Example

For better understanding, let us review some ohm’s law examples below.

1.) An electric iron draws 5 A at 20 V. Calculate its resistance.

Solution :

Using Ohm’s law :

    \begin{align*}R=\frac{v}{i}=\frac{20}{5}=4\Omega\end{align*}

2.) According to the circuit below, calculate the current (i) and the power (p).

ohm's law 7

Solution :

The current is :

    \begin{align*}i=\frac{v}{R}=\frac{12}{4}=3A\end{align*}

The power is :

    \begin{align*}p=vi=12\times3=36W\\&or\\p=i^{2}R=3^{2}\times4=36W\end{align*}

Frequently Asked Questions

What is Ohm’s law formula?

Ohm’s law formula is V=IR, where V is the voltage across an element, I is the current flowing through the element and R is the resistance provided by the element.

Ohm’s law exists only for which elements?

Just as its name implies, Ohm’s law is only usable to ohmic elements such as conductor wire (iron, copper). Ohm’s law is unusable to non-ohmic elements such as semiconductors (transistors).

How to calculate Ohm’s law?

To calculate Ohm’s law we can use voltage (V) = current (I) x resistance (R), resulting in V (volts) = A (ampere) x Ω (ohm).

What is Ohm’s law equation?

Ohm’s law equation is V = I x R, where V is voltage, I is current, and R is resistance.

What are the limitations of Ohm’s law?

The limitations of Ohm’s law are Can’t be used for a unilateral electrical network (diode transistor, etc) that doesn’t have linear voltage-current relationship and can’t be implemented for a nonlinear circuit.

In Ohm’s law the capital letter ”e” stands for what?

Voltage is represented by letters “E” or “V” and measured in volts. Then the Ohm’s law can be written by E = IR or V = IR.

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