If ' $C^{\prime}$ and ' $V^{\prime}$ represent capacity and voltage respectively then what are the dimensions of
$\lambda$, where $\frac{\mathrm{C}}{\mathrm{V}}=\lambda$ ?
$\left[\mathrm{M}^{-2} \mathrm{~L}^{-3} \mathrm{I}^{2} \mathrm{~T}^{6}\right]$
$\left[\mathrm{M}^{-3} \mathrm{~L}^{-4} \mathbf{I}^{3} \mathrm{~T}^{7}\right]$
$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{I}^{-2} \mathrm{~T}^{-7}\right]$
$\left[\mathrm{M}^{-2} \mathrm{~L}^{-4} \mathrm{I}^{3} \mathrm{~T}^{7}\right]$
Correct Option: , 4
$\lambda=\frac{\mathrm{C}}{\mathrm{V}}=\frac{\mathrm{Q} / \mathrm{V}}{\mathrm{V}}=\frac{\mathrm{Q}}{\mathrm{V}^{2}}$
$\mathrm{V}=\frac{\text { work }}{\mathrm{Q}}$
$\lambda=\frac{\mathrm{Q}^{3}}{(\text { work })^{2}}=\frac{(\mathrm{It})^{3}}{(\text { F.s })^{2}}$
$=\frac{\left[\mathrm{I}^{3} \mathrm{~T}^{3}\right]}{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]^{2}}=\left[\mathrm{M}^{-2} \mathrm{~L}^{-4} \mathrm{I}^{3} \mathrm{~T}^{7}\right]$
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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,