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 ( ).
E.g: Dimension formula of mass is: (M)
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
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)
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 M1 L1 T-2
The dimensional formula of charge = current × time = I1 T1
∴ The dimensional formula of voltage is written as (Force × Charge-1) × Distance
= (M1 L1 T-2) * (I1 T1)-1 * (L1) = (M1. L2. T-3. I-1).....(2)
On placing equation (2) in equation (1) we get,
Resistance (R) = Voltage × Current-1
Or, R = (M1. L2 .T-3. I-1) * (I)-1 = (M1. L2. T-3 .I-2)
Therefore, the resistance is dimensionally written as M L2 T-3 I-2.
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.
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
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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.