# What is Ohm’s Law? Theory and Formula

So, are you wondering why Ohm’s law is an important thing to learn?

What is Ohm’s law actually?

How to use it?

At first, we will get confused by its name, why it has to be Ohm’s law? I know that. The name itself comes from who discovered it for the first time.

This law exists to get a measurement of ‘Electrical Resistance’.

Contents

Ohm’s law is the most fundamental and the most basic law for electrical and electronic circuit. You can find all the basic elements in an electrical circuit, they are: voltage, current, and resistance.

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, the 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 is an electric circuit 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.

## What is Ohm’s Law

If you search what is ohm’s law formula, you will get these definitions:

Wikipedia:
a law stating that electric current is proportional to voltage and inversely proportional to resistance.

Collins Dictionary:
the principle that the electric current passing through a conductor is directly proportional to the potential difference across it, provided that the temperature remains constant. The constant of proportionality is the resistance of the conductor.

Ohm’s law formula or Ohm’s law equation 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.

Ohm’s law definition above don’t help much if we don’t know what is what. We need to know what variables do we use, what is the equation, and also how to use it.

From what we have found in the American English Dictionary, it states that Ohm’s Law is the proportional ratio of the current of a dc circuit to its applied voltage and inversely proportional to resistance. Not only to dc, the Ohm’s law applies to ac circuit.

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

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 insulator.

Resistance, measured in ohms, is determined by the material. Different material with different sizes provides different resistance one from 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 of 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) flows 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.

From Figure.(1a) we conclude that the uniform cross-sectional A material resistance depends on cross-sectional area A and the length l.

Hence, the mathematical equation of resistance can be seen below:

(1) Where:

ρ = resistivity of the material, measured in ohm-meters.

The lower the resistivities means the material has better conductivity as conductors.

The example of good conductors is aluminium and copper. Otherwise, the example of good insulators is mica and paper which have high resistivities.

If you want to know other examples of good conductors and good insulators, you can find it on the internet freely. Just go for it and remember them well.

Except for those two, we will learn about semiconductor materials, but let’s skip it for now.

If we are talking about resistance, we will mainly be talking about resistors. But what is it exactly? The resistor is the simplest passive element which is made from metallic alloys and carbon compounds to be able to resist the electric current.

Its circuit symbol can be seen in Figure.(1b), where R stands for the resistance value.

Ohm’s law presents the relationship between current and voltage to the resistor. This law is credited to Georg Simon Ohm (1787-1854) and written as:

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

Hence,

(2) For short,

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

## Voltage, Current, and Resistance

An electric circuit is made from a conductive wire to allow an electric charge to flow through it. The movement of this electric charge is called a current.

The electric force, called voltage, gives energy to the electric charge to flow in a circuit. For scientific explanation, voltage is a potential difference between two terminals (points).

If we measure the voltage, it means we measure the potential difference to move the electric charge from one point to another point.

If there are no two points, there is no voltage.

Current moves in a conductor path with some opposition or friction to it. This friction or opposition is known as resistance.

Even a conductor wire has small resistance for currents. The amount of current depends on how much the voltage and the resistance.

The lower the resistance, the higher the current.

## Units of Measurement: Volt, Amp, and Ohm

Having to know the terms of voltage, current, and resistance won’t do much for us. We need to understand the quantities for an electric circuit.

Below are the standard units of measurement for electrical voltage, current, and resistance: The abbreviation for each measurement is close to their first word. The abbreviation for voltage is “V” and “R” for “resistance”. While “I” is a bit weird because it is far from current.

The “I” stands for a French phrase “intensité du courant” (current intensity). We will find another symbol “E” that stands for “Electromotive force”.

Both “V” and “E” are the same, but we will use “V” instead. It is a common thing that “E” is the terms of voltage across a source.

Those abbreviations are written in capital letters because we will use DC terms here. Capital letters mean the value is constant for a period of time.

But, we will use lowercase letter if they have periodic value for a periodic time.

## Ohm’s Law Equation

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.

We need the simplest circuit example to master this basic law. We will use the simple circuit below to explain Ohm’s law equation, consisting of a voltage source and a resistor. The current is represented by I and measured in amperes (A), equal to the voltage (V) divided by the resistance of the resistor (R) measured in ohms (Ω).

Hence, the Equation.(2) becomes

(3) which is the mathematical equation of Ohm’s law. Thus, R in Equation.(3) is measured in ohms or Ω.

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

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

R is the 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

(4) so that

1 Ω = 1 V/A

In order to successfully implement the Ohm’s law formula used to find resistance, we need to pay attention to voltage polarity or current flow direction.

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 in Figure.(2a) is a short circuit.

So,

(5) indicating that the voltage is zero but the current could be any values. 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 seen in Figure.(2b). For an open circuit,

(6) indicating that the current is zero through the voltage could be any values. Hence,

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

## How Does Ohm’s Law Work?

Ohm’s law is an analysis method to analyze the currents in a circuit with a certain resistance supplied by a voltage source. For an analogy, we can imagine using a water pipe.

The water pressure is the voltage source, the resistance is the pipe’s diameter, while the current is the volume of the water.

Higher voltage will provide higher current and vice versa. But, higher resistance will provide a lower current.

This proves the proportional ratio between voltage and current, but the inverse proportional ratio between current and resistance.

## Ohm’s Law Simple Problems

Check out these simple problems to give you a better understanding of Ohm’s law.

1. If we have an electric circuit with a constant voltage source and increase the resistance, what will happen to the current?

Answer: scroll up and read the ohm’s law equation if you forgot about it. From the current perspective, we will use [I = V/R]. If the voltage remains constant but the resistance is increased, then the current will decrease.

1. If the voltage source is doubled, how much current we get?

Answer: using the same equation [I = V/R], if the V became 2V then the current is 2V/R. Thus, the current is doubled.

## Ohm’s Law Circuit Analysis

Let us try to analyze an electric circuit using Ohm’s law. Don’t worry, we will just use a battery, a resistor, and a conducting wire.

The current moves in a clockwise direction because the voltage polarity is in the top left side. Those three are connected in series to make it easier.

Imagine if we have a 10V battery and a 5-Ω resistor, how much is the current? The equation is valid because if you use [I = V/R] then you get [I = 10/5 = 2 A].

What will happen if we replace the resistor with a 10-Ω resistor? And again, the ohm’s law is valid for giving the 1A result.

We can interchange the variable equation as long as it fulfils the Ohm’s law triangle which you will read about later in this post. We will use this law for a circuit with multiple resistors connected by:

• Series connection
• Parallel connection

## Ohm’s Law Triangle Method

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. 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 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 Application

Just from the explanation above, we can conclude that Ohm’s law is useful for finding the value of voltage, current, and resistance.

But, how does it help us in real life? Below is the applications of Ohm’s law in real life:

• Finding voltage, current, and resistance in a circuit.
• Maintain the voltage drop across the circuit element for the desired value.
• This law is applied for dc ammeters.

## 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.

## Type of Resistor

A resistor can be either fixed or variable. But, it has fixed value which means the value remains constant. Figure.(3) shows the two common types of fixed resistors (wirewound and composition). A single resistor will form a branch in the circuit.

The Figure.(3a) is wirewound type has smaller resistance with larger power threshold while the Figure.(3b) is a composition type, has higher resistance with smaller power threshold.

Variable resistors have adjustable resistance and its symbol can be seen in Figure.(4a).

A common variable resistor is also known as potentiometer or pot for short, its symbol is shown in Figure.(4b).

The pot is a three-terminal element with sliding contact or wiper. Using the sliding contact will change the resistance. Similarly, the variable resistor also has a type of wirewound and composition as can be seen in Figure.(5a) for composition and Figure.(5b) for slider pot.

Not all resistors obey Ohm’s law. But, a resistor that obeys Ohm’s law is called a linear resistor. It has constant resistance.

Hence, its current-voltage characteristic can be seen in Figure.(6a) : the i-v graph is a straight line passing the origin.

A nonlinear resistor does not obey Ohm’s law, its resistance varies with current and its i-v characteristic can be seen in Figure.(6b).

An example of nonlinear resistance is light bulb and diodes.

## Conductances

Another useful quantity in electric circuit analysis is reciprocal of resistance R, known as conductance and the symbol is G :

(7) Conductance measures how well an element will conduct electric current and its unit is mho (ohm spelt backwards) or reciprocal ohm with the symbol ℧, an inverted omega.

In this blog we will use siemens (S) over mho, as SI unit of conductance :

(8) Hence,

Conductance is the ability of an element to conduct electric current; measured in mhos (℧) or siemens (S)

Same resistance can be expressed in ohms or siemens, for example, 10 Ω is the same as 0.1 S. Looking from Equation.(7) we can write :

(9) The power dissipated by a resistor can be expressed using R with Equation.(3),

(10) The power dissipated by a resistor can be expressed using G,

(11) ## Ohm’s Law Linear Graph

We can draw the Ohm’s law graph with 2D axis, voltage and current as shown below. The voltage and current will form a linear graph for every types of resistor we use, may it fixed resistor, variable resistor, or just a simple wire with various length. We can conclude that doubling the voltage will double the current flowing through the circuit element.

## Ohm’s Law Examples

1.) An electric iron draws 2 A at 120 V. Calculate its resistance.

Solution :

Using Ohm’s law : 2.) According to the circuit below, calculate the current i, the conductance G, and the power p. Solution :
The current is : The conductance is : The power is : ### WHAT IS A in ohm’s law?

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.

### How do you calculate ohm’s law?

The current (I) in a circuit is equal to the voltage (V) across in a resistor and divided by the resistance (R) of the resistor.

### Why is Ohm’s law important?

Ohm’s law is very important for analyzing an electric circuit related to the voltage, current, and resistance in a circuit and finding their relationship.

### What is Ohm’s law Short answer?

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

### Is Ohm’s law applicable to both AC and DC?

Ohm’s law states that the current in a circuit is proportional to voltage and inversely proportional to the resistance. This means as long as the voltage and current has a linear relationship, Ohm’s law can be used for AC circuits.

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