Let $I=$ current through a conductor, $R=$ its resistance and $V=$ potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for $R$ and $V$ are $\left[\mathrm{ML}^{2} \mathrm{I}^{-2} \mathrm{~T}^{-3}\right]$ and $\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~J}^{-1}\right]$ respectively
Dimension of $\mathrm{R}=\left[\mathrm{ML}^{2} \mathrm{I}^{-2} \mathrm{~T}^{-3}\right]$
Dimension of $\mathrm{V}=\left[\left.\mathrm{ML}^{2} \mathrm{~T}^{-3}\right|^{-1}\right]$
Now, $R=\left[\mathrm{ML}^{2} \mathrm{I}^{-2} \mathrm{~T}^{-3}\right]=\left[\mathrm{ML}^{2} \mathrm{I}^{-1} \mathrm{~T}^{-3}\right] /[I]=\mathrm{V} /[\mathrm{I}]=\mathrm{V} / \mathrm{I}$ or, $V=I R$.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,