The resistivity of resistive wire is ρ=(AR / L) where L= length of wire A= Area of wire and R is

Name: Problem 156, Chapter 1: JEE Physics
Uploaded: 2021-10-05T18:20:58-08:00
Duration: 1 min 5 s
Channel: Mirza Aslam Beig
Description: The resistivity of resistive wire is ρ=(AR / L) where L= length of wire A= Area of wire and R is resistance of wire find dimension formula of ρ(a) M^1 L^3 T^-3 A^-2 (b) M^1 L^2 T^-3 A^-2 (c) M^2 L^3 T^1 A^2 (d) M^2 L^3 T^-3 A^-2

step 1 Okay, in this question we are asked that resistivity of resistive wire is R equal to A out of L

Question

The resistivity of resistive wire is $\rho=(\mathrm{AR} / \mathrm{L})$ where $L=$ length of wire $A=$ Area of wire and $R$ is resistance of wire find dimension formula of $\rho$ (a) $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ (b) $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ (c) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{1} \mathrm{~A}^{2}$ (d) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$

   The resistivity of resistive wire is $\rho=(\mathrm{AR} / \mathrm{L})$ where $L=$ length of wire $A=$ Area of wire and $R$ is resistance of wire find dimension formula of $\rho$
(a) $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
(b) $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
(c) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{1} \mathrm{~A}^{2}$
(d) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$

JEE Physics

StemEZ 1st Edition

Chapter 1, Problem 156

Instant Answer

Solved by Expert Mirza Aslam Beig

10/05/2021

Step 1

We know that the dimensions of area (A) is $L^2$, the dimensions of resistance (R) is $M L^2 T^{-3} A^{-2}$, and the dimensions of length (L) is $L$. Show more…

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The resistivity of resistive wire is $\rho=(\mathrm{AR} / \mathrm{L})$ where $L=$ length of wire $A=$ Area of wire and $R$ is resistance of wire find dimension formula of $\rho$ (a) $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ (b) $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ (c) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{1} \mathrm{~A}^{2}$ (d) $\mathrm{M}^{2} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$

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Key Concepts

Resistivity

Resistivity is a material property that quantifies how strongly a material opposes the flow of electric current. It is defined through the relation ? = (R A / L) and is expressed in terms of ohm-meters in the SI system. Its dimensional formulation is derived by substituting the dimensions of resistance, area, and length.

Electric Resistance

Electric resistance is a measure of the opposition to current flow in an electrical circuit. Its dimensions stem from the fundamental relation between voltage and current (Ohm’s law), and in SI units the resistance has dimensions represented as M L² T?³ I?².

Dimensional Analysis

Dimensional analysis is a method used to verify the consistency of physical equations by comparing the dimensions on both sides. It involves expressing complex physical quantities in terms of base dimensions such as mass (M), length (L), time (T), and electric current (I) to derive relationships or check the validity of derived formulas.

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