A capacitor is connected to a $20 \mathrm{~V}$ battery through a resistance of $10 \Omega$. It is found that the potential difference across the capacitor rises to $2 \mathrm{~V}$ in $1 \mu \mathrm{s}$. The capacitance of the capacitor is___________ $\mu \mathrm{F} .$
Given : $\ln \left(\frac{10}{9}\right)=0.105$
$9.52$
$0.95$
$0.105$
$1.85$
Correct Option: , 2
$\mathrm{V}=\mathrm{V}_{0}\left(1-\mathrm{e}^{-\mathrm{t} / \mathrm{RC}}\right)$
$2=20\left(1-\mathrm{e}^{-\mathrm{t} / \mathrm{RC}}\right)$
$\frac{1}{10}=1-\mathrm{e}^{-\mathrm{t} / \mathrm{RC}}$
$\mathrm{e}^{-\mathrm{t} / \mathrm{RC}}=\frac{9}{10}$
$\mathrm{e}^{\mathrm{t} / \mathrm{RC}}=\frac{10}{9}$
$\frac{\mathrm{t}}{\mathrm{RC}}=\ln \left(\frac{10}{9}\right) \Rightarrow \mathrm{C}=\frac{\mathrm{t}}{\mathrm{R} \ln \left(\frac{10}{9}\right)}$
$\mathrm{C}=\frac{10^{-6}}{10 \times .105}=.95 \mu \mathrm{F}$
Option (2)
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- Alternating Current
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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,