What is Ohm’s Law? Theory and Formula

ohm law triangle

Now we will start to learn the most basic electric circuit analysis method: Ohm’s law and Kirchoff’s laws. But, we will save Kirchoff’s laws for later.

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’.

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.

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.

What is Ohm’s Law

If you search what is ohm’s law, 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.

Definitions 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.

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 law resistance
Figure 1. Resistance

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:

ohm law resistivity
(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,

ohm law
(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:

ohm law measurement unit

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.

Hence, the Equation.(2) becomes

ohm's law formula
(3)

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

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

ohm law equation
(4)

so that

1 Ω = 1 V/A

In order to successfully implement the Ohm’s law, 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:

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)

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.

ohm law short circuit
Figure 2. Short circuit

So,

ohm law short circuit
(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,

ohm law 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.

2. 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?

ohm law circuit analysis

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?

ohm law circuit analysis

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.

ohm 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 law triangle

Ohm’s Law Wheel

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 law wheel

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.

ohm law fixed resistor
Figure 3. Fixed resistor

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).

ohm law variable resistor
Figure 4. Variable resistor

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.

ohm law potentiometer
Figure 5. Potentiometer

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.

ohm law resistor v i relationship
Figure 6. Resistor i-v characteristic

Conductances

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

ohm law conductances
(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 :

ohm law conductances
(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 :

ohm law conductances
(9)

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

ohm law conductances
(10)

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

ohm law conductances
(11)

Ohm’s Law Examples

1. An electric iron draws 2 A at 120 V. Calculate its resistance.
Solution :
Using Ohm’s law :
resistance example
 
2. According to the circuit below, calculate the current i, the conductance G, and the power p.
current voltage example
 
Solution :
The current is :
electric current example solution
The conductance is :
conductance example
The power is :
power example solution

Frequently Asked Questions:

Now let us answer the most frequently asked questions below:

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.

Have you understood what is ohm’s law? Don’t forget to share and subscribe! Happy learning!

Reference:  Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku