Dimensional formula of resistance

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, trigono...

As per Ohm’s law V = iR. In this formula, V is the potential difference and i is current and R is resistance. According to this law, R= Vi. when this formular to used to find the dimensional formula of R. V is equal to the work done per unit charge. In this formula when a conductor with a resistance existence and R is connected across a cell of emf V. A potential difference will be created by the cell across the conductor and due to the potential difference, a current will be created in the circuit. If resistance is R and the current in the circuit is i, then, Ohm’s law will be applied, V = iR. Hence [R]=[ML2T−3A−1] and [A]=[ML2T−3A−2]. Answer: The dimensions of electrical resistance is =[M1L2T−3A−2] The electrical resistance of a given substance can be defined as the ability of the substance to resist the flow of electrons or charges. When a potential difference is created across the substance resistance may occur. In such cases, the flow of charges per unit of time can be defined as current in the circuit. Summary: The dimensions of electrical resistance are: The dimensions of electrical resistance is =[M1L2T−3A−2].As per Ohm’s law V = iR. In this formula, if resistance is R and the current in the circuit is i, then, Ohm’s law will be applied, V = iR. Hence [R]=[ML2T−3A−1] and [A]=[ML2T−3A−2].

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F09%253A_Current_and_Resistance%2F9.04%253A_Resistivity_and_Resistance \( \newcommand\) • • • • • • • • • • • • • • • • Learning Objectives By the end of this section, you will be able to: • Differentiate between resistance and resistivity • Define the term conductivity • Describe the electrical component known as a resistor • State the relationship between resistance of a resistor and its length, cross-sectional area, and resistivity • State the relationship between resistivity and temperature What drives current? We can think of various devices—such as batteries, generators, wall outlets, and so on—that are necessary to maintain a current. All such devices create a potential difference and are referred to as voltage sources. When a voltage source is connected to a conductor, it applies a potential difference V that creates an electrical field. The electrical field, in turn, exerts force on free charges, causing current. The amount of current depends not only on the magnitude of the voltage, but also on the characteristics of the material that the current is flowing through. The material can resist the flow of the charges, and the measure of how much a material resists the flow of charges is known as the resistivity. This...

CONCEPT: • Dimensional formula:Itis a compound expression showing how and which of the fundamental quantities are involved in making that physical quantity. Quantity Dimensional formula Force (F) [MLT -2] Electric charge (Q) [AT] Electric potential/Voltage (V) [ML 2 T -3 A -1 ] Surface tension (S) [ML 0T -2] Spring constant (K) [ML 0T -2] Angular frequency(ω) [T -1] Energy (E) [ML 2T -2] Resistance (R) [ML 2 T -3 A -2 ] Plank's constant [ML 2 T -1 ] CALCULATION: • In the options, h is the Plank constant and e is the charge of an electron. Hence • Dimensional formula of e or charge Q = [AT] • Dimensional formula of h = [ML 2 T -1 ] • Dimensional formula of Resistance = [ML 2T -3A -2] • Dimension of \( ]\) • So the dimension of h/e 2 is the same as the Resistance. • Hence the correct answer is option 1.

Assertion : The dimensional formula for product of resistance and conductance is same as for dielectric constant. Reason : Both have dimensions of time constant (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is not correct explanation of A (c) A is true but R is false (d) A and R are false