## Dimensions

Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity.

### Dimensional Formula

The dimensional formula of any physical quantity is that expression that represents how and which of the base quantities are included in that quantity.

It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e ( ).

E.g: Dimension formula of mass is: (M)

### Dimensional Equation

The equation obtained by equating a physical quantity with its dimensional formula is called a dimensional equation.

### Application of Dimensional Analysis

To convert a physical quantity from one system of the unit to the other:

It is based on a fact that the magnitude of a physical quantity remains the same whatever system is used for measurement i.e magnitude = numeric value(n) multiplied by unit (u) = constant

n1u1= n1u2

To check dimensional correctness of a given physical relation:

If in a given relation, the terms of both sides have the same dimensions, then the equation is dimensionally correct. This concept is best known as the principle of homogeneity of dimensions.

To derive a relationship between different physical quantities:

Using the principle of homogeneity of dimension, the new relation among physical quantities can be derived if the dependent quantities are known.

### Limitation of this Method

This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. The formula containing more than one term which is added or subtracted likes s = ut+ ½ at2 also cannot be derived.

The relation derived from this method gives no information about the dimensionless constants.

### Dimension of Resistance

Dimension formula of resistance is: length × mass × time-3 × electric-current-2 (M1 L2 T-3 I-2)

Where,

M = Mass

I = Current

L = Length

T = Time

### Derivation of Resistance Dimension

Resistance (R) = Voltage × Current-1 . . . . (1)

As we all know the formula of voltage (V) = Electric Field × Distance = (Force × Charge-1) × Distance

The dimension formula of force can be written as M^{1} L^{1} T^{-2}

The dimensional formula of charge = current × time = I^{1} T^{1}

∴ The dimensional formula of voltage is written as (Force × Charge-1) × Distance

= (M^{1} L^{1} T^{-2}) * (I^{1} T^{1})^{-1} * (L^{1}) = (M^{1}. L^{2}. T^{-3}. I^{-1}).....(2)

On placing equation (2) in equation (1) we get,

Resistance (R) = Voltage × Current-1

Or, R = (M^{1}. L^{2} .T^{-3}. I^{-1}) * (I)^{-1} = (M^{1}. L^{2}. T^{-3} .I^{-2})

Therefore, the resistance is dimensionally written as M L^{2} T^{-3} I^{-2}.

### Define Resistance

The resistance of the conductor is the opposition offered by a conductor during the flow of change. When the potential difference is applied across the conductor, free electrons get accelerated and collide with positive ions and their motion is thus opposed. This opposition offered by ions is called the resistance of the conductor. Hence the resistance is the property of the conductor by which it opposes the flow of current in it.

Unit of resistance is the ohm.

### Factors on which Resistance is Dependent

Length of the conductor.

Area of a cross-section of the conductor.

It is dependent on the material of the conductor but does not depend on the geometry of the conductor.

The resistance of the conductor depends on the temperature of the conductor.

### Resistivity

The specific resistance of the material is equal to the resistance of the wire of that material unit cross-section area and unit digit.

### Factors on which Resistivity Depends

1. Nature of material.

2. Temperature of material.

### Studying the Concept of Dimension of Resistance

Studying the concept of Dimension of Resistance can be a little time-consuming. With Vedantu’s e-learning platform, you can learn this concept in no time and be more efficient. Vedantu proffers an unlimited stock of study materials to help you study the Dimension of Resistance Formula, Equation, Application, Limitation and Factors, and other concepts of Physics. Besides Vedantu, below are some other tips that will aid you in learning this topic.

You can start learning the concept of Dimension of Resistance directly from Vedantu’s online learning platform that provides you with detailed explanations in simple language to make the concept easy to understand.

When you are studying the Dimension of Resistance make sure you note down all the essential information in your words and simplify the explanations.

Refer to the notes of Dimension of Resistance while preparing for your exam for a quick revision.

Practice the questions based on Dimension of Resistance regularly to improve your understanding of the topic.

Once you have completed the Dimension of Resistance, you should use the textbook exercises to test your knowledge and check if you have understood the concept properly or not.

Go through sample papers and previous year question papers to understand the difficulty level of questions related to Dimension of Resistance.

Use reference books and guides that will give you a deep insight into the concept of Dimension of Resistance enhance your knowledge.

### Significance of Dimension

The Dimension of Resistance – Is one of the most important concepts of Physics. In this topic, you will learn about resistance, dimensions of resistance formula, applications of that formula, and much more. Once you go through this topic, you will understand why the dimensional formula of resistance is important and what are its advantages and disadvantages. Besides this, you will also be able to apply this formula into equations and solve questions, based on Dimension of Resistance Formula, Equation, Application, Limitation, and Factors, with ease. Here are some reasons why you should not skip this topic before the exam:

The Dimension of Resistance – Is among the most important topics covered in the IIT JEE syllabus. So, if you have a strong grasp of this concept, you can score really well in your IIT JEE exam.

Learning more about resistance and the dimensional formula of resistance will enhance your knowledge of the Physics subject that covers a major portion of the IIT JEE exam question paper.

Once you go through the Dimension of Resistance thoroughly, you won’t have to read the entire concept again during exam preparations.

If you have a good understanding of the dimensional formula of resistance and its applications, you will be able to solve the practical questions in your IIT JEE exam with ease.

## FAQs on Dimension of Resistance

**1. Define Dimension Formula.**

Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity. The dimensional formula of any physical quantity is that expression that represents how and which of the base quantities are included in that quantity.

It is written by enclosing the symbols for base quantities with appropriate power in square brackets i.e ( ).

**2. Explain a Few Limitations of Dimension Formulas.**

Some of the limitations of the dimension formula are given below:

This method can be used only if dependency is of multiplication type. The formula containing exponential, trigonometric, and logarithmic functions can not be derived using this method. A formula containing more than one term which is added or subtracted likes \[s= ut + \frac{1}{2}\] at 2 also cannot be derived.

The relation derived from this method gives no information about the dimensionless constants.

**3. Write a few sets that have the same Dimension Formula.**

Some of the sets having the same dimension formula that are discussed below:

Strain, refractive index, relative density, angle, solid angle, phase, distance gradient, relative permeability, angle of content.

Mass and inertia.

Momentum and impulse.

Thrust, force, weight, tension, energy gradient.

Angular momentum and plaques contant.

Surface tension, surface area, force gradient, spring constant.

Latent heat and gravitational potential.

Thermal capacity, Boltzman constant, entropy.

**4. Is it necessary to learn the Dimension of Resistance? **

Yes, it is necessary to learn the Dimension of Resistance because for a number of reasons. This concept gives you a better understanding of resistance and the dimensional formula of resistance. You can learn how this formula is applied in different areas and what are its advantages and limitations. Moreover, in some previous year questions of the IIT JEE exam, many questions have been asked from the Dimension of Resistance. So, by learning this concept you will be able to secure an excellent score in your exam.

**5. From where can I learn the concept of Dimension of Resistance?**

Vedantu is the best online educational platform to learn the concept of Dimension of Resistance. On our platform, you can find notes on this topic in simple language that will help you understand the concept more clearly and easily. To learn the Dimension of Resistance, all you have to do is visit Vedantu.com and search for it. There will be no registration amount, whether you use our website or the mobile application. Moreover, Vedantu provides you with the best study materials to learn other concepts covered in the IIT JEE exam question paper. With Vedantu, you can get IIT JEE sample papers, previous year question papers, important topics, revision notes, and much more for absolutely free.