A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
Capacitance of a charged capacitor, $C_{1}=4 \mu \mathrm{F}=4 \times 0^{-6} \mathrm{~F}$
Supply voltage, V1 = 200 V
Electrostatic energy stored in C1 is given by,
$E_{1}=\frac{1}{2} C_{1} V_{1}^{2}$
$=\frac{1}{2} \times 4 \times 10^{-6} \times(200)^{2}$
$=8 \times 10^{-2} \mathrm{~J}$
Capacitance of an uncharged capacitor, $C_{2}=2 \mu \mathrm{F}=2 \times 0^{-6} \mathrm{~F}$
When C2 is connected to the circuit, the potential acquired by it is V2.
According to the conservation of charge, initial charge on capacitor C1 is equal to the final charge on capacitors, C1 and C2.
$\therefore V_{2}\left(C_{1}+C_{2}\right)=C_{1} V_{1}$
$V_{2} \times(4+2) \times 10^{-6}=4 \times 10^{-6} \times 200$
$V_{2}=\frac{400}{3} \mathrm{~V}$
Electrostatic energy for the combination of two capacitors is given by,
$E_{2}=\frac{1}{2}\left(C_{1}+C_{2}\right) V_{2}^{2}$
$=\frac{1}{2}(2+4) \times 10^{-6} \times\left(\frac{400}{3}\right)^{2}$
$=5.33 \times 10^{-2} \mathrm{~J}$
Hence, amount of electrostatic energy lost by capacitor C1
= E1 − E2
= 0.08 − 0.0533 = 0.0267
= 2.67 × 10−2 J
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- 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
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- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,