For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the
dielectric slab is $\frac{3}{4} \mathrm{~d}$, where ' $\mathrm{d}$ ' is the separation
between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C0 ) is given by the following relation :
$\mathrm{C}^{\prime}=\frac{3+\mathrm{K}}{4 \mathrm{~K}} \mathrm{C}_{0}$
$\mathrm{C}^{\prime}=\frac{4+\mathrm{K}}{3} \mathrm{C}_{0}$
$\mathrm{C}^{\prime}=\frac{4 \mathrm{~K}}{\mathrm{~K}+3} \mathrm{C}_{0}$
$C^{\prime}=\frac{4}{3+K} C_{0}$
Correct Option: 3,
$C_{0}=\frac{\epsilon_{0} A}{d}$
$\mathrm{C}^{\prime}=\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ in series.
i.e. $\frac{1}{C^{\prime}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}$
$\frac{1}{\mathrm{C}^{\prime}}=\frac{(3 \mathrm{~d} / 4)}{\epsilon_{0} \mathrm{KA}}+\frac{\mathrm{d} / 4}{\epsilon_{0} \mathrm{~A}}$
$\frac{1}{C^{\prime}}=\frac{d}{4 \in_{0} A}\left(\frac{3+K}{K}\right)$
$C^{\prime}=\frac{4 K C_{0}}{(3+K)}$
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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,