Unit of Resistance

Resistance is a physical property of a material due to which, the material resists the flow of electricity through it. Resistance depends on the physical dimensions of the material, its composition, and temperature. The fundamental property resistivity or specific resistance is a measure of the resistance offered by a material. The resistance of a conductor is very low whereas insulators have very high resistances. The resistance of a conducting wire is proportional to its length and inversely proportional to its cross-sectional area. Resistance is a scalar quantity and it is expressed using a number with appropriate units. The SI unit of resistance is Ohm.

Definition of Resistance: Ohm’s Law

Ohm’s law states that the current flowing through a conductor is proportional to the potential difference between the two ends of the conductor, given that the temperature and other physical quantities remain constant. Mathematically, if the potential difference between the ends of a conductor is V, the current I flowing through it is,

I∝V

The proportionality constant is given by, 

V/I = R

R is called the resistance of the conducting wire, which depends on the physical state and composition of the constituent material.

Dimension and Unit of Resistance Formula

The SI unit of resistance is Ohm(Ω), named after Georg Ohm. If 1 A of current flows through the ends of a conductor when the two ends are kept at 1 V of potential difference, the resistance of the conductor is defined as 1 Ohm.

1 Ω  = 1V/1A

In terms of fundamental units, Ohm can be expressed as,

\[\Omega = \frac{J}{SA^{2}}\]

   =kg.m².s^-3.A²

The dimension of resistance is \[ML²\]\[T^-3\]\[I^-2\]. 

International Ohm Unit Definition

The resistance of a column of mercury, which has a temperature of melting ice, uniform cross-sectional area, length of 106.3 cm, and mass of 14.4521 g, is called 1 Ohm.

SI Unit of Conductance

Electrical conductance is defined as the reciprocal of resistance. It is a property of a material that quantifies how easily current can conduct through the material. The SI unit of conductance in siemens (S) or mho, which is the inverse of ohm, is the SI unit of electrical resistance.

mho = 1/ohm

         = A/V

Specific Resistance

The resistance R of a conductor depends on its length L, cross-section A, and its composition. For a fixed cross-section, the resistance is proportional to the length of the conductor. Whereas the resistance is inversely proportional to the cross-section for a fixed length. These two dependencies can be written down combinedly as,

R∞L/A

R = pL/A

Here, is a proportionality constant, which is known as the specific resistance.  The resistance of a homogeneous chunk of a material of unit length and unit cross-section is defined as the resistivity or specific resistance of the material. Quantitatively,

p = RA/L

The SI unit of specific resistance is Ohmm (Ω.m).

Resistance Unit Conversion Table

CGS unit of resistance is esu of resistance or statohm (stat Ω). It is related to ohm as,

1 Ω = 1V/1A

       = (1/300statV)/(3×109statA)

       = 1/9 X( 10¹¹) stat Ω

1 stat Ω = 9 X 10¹¹ Ω

Another unit of resistance is emu of resistance and it is related to ohm as,

1 emu of resistance = 1emuofpotential/1emuofcurrent

                   = 10^-8V/10A

                   = 10^-9Ω

Some Useful Units are listed Below

Solved Examples

A 5 mm diameter wire is produced from a chunk of metal. Another wire of diameter 1 cm is produced from an identical chunk. What is the ratio of the resistance of the two wires?

Resistance of a wire of length L  and cross-section A  is p/LA, which is the resistivity of the material. The mass and density of the chunk are m and  D respectively. If the diameter of a wire of volume V is d,

A = πd2/4

V= m/D

L = V/A

Therefore, the resistance of a wire of diameter d is,

R = 16pm/πDd4

According to the problem, the mass and density of the two wires of diameters d1 = 5 mm=0.5cm and d2 =1 cm are the same such that the ratio of resistance is,

R1/R2 = (d2/d1)4

R1/R2 = (1cm/0.5cm)4

R1/R2 = 16

The ratio of the resistance of the wires is 16:1.

A parallel combination of two wires, made up of the same material, is connected to a battery. If the ratio of lengths and radii of the two wires are 4/3 and 2/3 respectively, what is the ratio of currents flowing through the wires?

Resistance of a wire of length L and radius r is,

R = pL/A = pL/πr2

where,   is the resistivity of the material.

The ratio of lengths L1 and L2 of the two wires is,

L1/L2 = 43

The ratio of radii r1 and r2  of the two wires is,

r1/r2 = 23

Since the two wires are made up of the same material, the values are the same for both of them. The ratio of resistance r1 and r2 is

r1/r2  =  (L1/L2).(r2r1)2

            =(4/3). (3/2)2

            = 3

In a parallel combination of resistors, the current flowing through one conductor is inversely proportional to its resistance i.e. the ratio of currents L1 and L2 is,

I1/I2 = R2/R1 = ⅓

The ratio of magnitudes of current flowing through the wires is 1:3.

Did You know?

Resistance depends on temperature. If other physical quantities are held constant, resistance increases with increasing temperature for metals. For glass, however, at very high temperatures, the resistivity decreases considerably.

Superconductors have zero resistance in the superconducting state (at very low temperatures).

The resistivity of semiconductors decreases with increasing temperature.

Why Should You Learn the Unit of Resistance - Ohm’s Law and Specific Resistance?

Learning the Unit of Resistance - Ohm’s Law and Specific Resistance will give you a better understanding of electric currents. These concepts will help you understand the different aspects of resistance and resistivity. Ohm’s law is one of the most important laws of physics, which is why you must have a strong grasp of this topic. Below are the reasons why you should learn: 

• It gives you a deep insight into some of the most crucial topics of the Physics subject. 

• It carries a significant weightage in your exam. So, to score well in the exam, you must know everything about resistance, Ohm’s law, and other concepts explained above. 

• Once you have learned it, you will be able to solve the important questions related to these topics. 

• If you do not know anything about it, you will not be able to study subsequent chapters of the Physics subject. 

• You can study the examples related to it provided above to understand how to solve different kinds of questions based on these concepts. 

• Learning Ohm’s law will help you understand the relationship between current, voltage, and resistance in an electric circuit. This way, you will be able to determine voltage, current, or resistance when any two of the quantities are given in the question.  

Tips to start learning 

It can be a tricky concept to learn. However, Vedantu provides you with a user-friendly learning platform to help you learn this topic with ease. You can use the following tips and tricks to start learning this unit:

• While studying this unit, start making notes of the important points. These notes will come in handy during late revisions when you are preparing for your final exams. 

• After you are done with this, start solving important questions and questions that came in previous year papers. 

• Use Vedantu’s free learning platform to gain access to the notes and explanations of the Unit. These topics are explained by some of the best teachers at Vedantu to make the learning process smooth for students. 

• Refer to the examples related to this Unit to understand how to solve different types of questions in your exam.

• Try to clear all the doubts to ensure that you have a clear understanding of every concept. 

• Find as many questions as possible to practice and strengthen your grip on the topics.