energy stored in inductor derivation class 12

(i)Then, the magnitude of induced emf is,           ε = B.l.v             = 0.3 × 8 × 10-2 × 10-2= 2.4 × 10-4V Time for which induced e.m.f. © The work done is equal to the potential energy stored in the inductor. Pradhan. \begin{align*} \text {i.e.} 01.02 Conductors, Semiconductors and Insulators, 01.03 Basic Properties of Electric Charge, 01.08 Electric field due to a system of charges, 01.09 Electric Field Lines and Physical Significance of Electric Field, 01.11 Electric Dipole, Electric Field of Dipole, 01.13 Continuous charge distribution: Surface, linear and volume charge densities and their electric fields, 01.15 Field due to an infinitely long straight uniformly charged wire, 01.16 Field Due to Uniformly Charged infinite Plane Sheet, 01.17 Electric Field Due to Uniformly Charged Thin Spherical Shell, 3.04 Limitation of Ohm’s law, Resistivity, 3.05 Temperature dependence of Resistivity, 3.06 Ohmic Losses, Electrical Energy and Power, 4.02 Magnetic Force on Current Carrying Conductor, 4.03 Motion of a Charge in Magnetic Field, 4.07 Magnetic Field on the Axis of Circular Current Carrying Loop, 4.09 Proof and Applications of Ampere’s Circuital Law, 4.12 Force Between Two Parallel Current Carrying Conductor, 4.13 Torque on a rectangular current loop with its plane aligned with Magnetic Field, 4.14 Torque on a rectangular current loop with its plane at some angle with Magnetic Field, 4.15 Circular Current Loop as Magnetic Dipole, 4.16 The Magnetic Dipole Moment of a Revolving Electron, 4.18 Conversion of Galvanometer to Ammeter and Voltmeter, 5.03 Bar magnet as an equivalent solenoid, 5.04 Magnetic dipole in a uniform magnetic field, 5.07 Magnetic Declination and Inclination, 5.08 Magnetization and Magnetic Intensity, 5.09 Magnetic Susceptibility and Magnetic Permeability, 5.10 Magnetic Properties of Materials – Diamagnetism, 5.11 Magnetic Properties of Materials – Paramagnetism, 5.14 Permanent Magnets and Electromagnets, 6.02 Magnetic Flux And Faraday’s Law of Electromagnetic induction, 6.05 Motional EMF and Energy Consideration, 7.04 Representation of AC current and Voltages: Phasor Diagram, 7.09 AC Voltage applied to Series LCR Circuit: Phasor Diagram Solution, 7.10 AC Voltage applied to Series LCR Circuit: Analytical Solution, 7.13 Power in AC Circuit: The Power Factor, 7.14 LC Oscillator – Derivation of Current, 7.15 LC Oscillator – Explanation of Phenomena, 7.16 Analogous Study of Mechanical Oscillations with LC Oscillations, 7.17 Construction and Working Principle of Transformers, 7.18 Step Up, Step Down Transformers, and Limitations of Practical Transformer, 8.01 Introduction to Electromagnetic Waves, 8.04 Maxwell’s Equations and Lorentz Force, 8.07 Electromagnetic Spectrum: Radio Waves, Microwaves, 8.08 Electromagnetic Spectrum: Infrared Waves and Visible Light, 8.09 Electromagnetic Spectrum: Ultraviolet Rays, X-rays and ƴ-rays, 02 Electrostatic Potential and Capacitance, 2.07 Relation between Electric field and Electric potential, 2.08 Expression for Electric Potential Energy of System of Charges, 2.10 Potential energy of a dipole in an external field, 2.16 Series and Parallel Combination of Capacitors, 9.01 Reflection of Light by Spherical Mirrors: Introduction, Laws and Sign Convention, 9.06 Applications of Total Internal Reflection: Mirage, sparkling of diamond and prism, 9.07 Applications of Total Internal Reflection: Optical fibres, 9.09 Refraction by Lens: Lens-maker’s formula, 9.10 Lens formula, Image Formation in Lens, 9.11 Linear Magnification and Power of Lens, 9.12 Combination of thin lenses in contact, 9.14 Angle of Minimum Deviation and its Relation with Refractive Index, 9.16 Some Natural Phenomena due to Sunlight : The Rainbow, 9.17 Some Natural Phenomena due to Sunlight : Scattering of Light, 10.01 Wave Optics: Introduction and Historical Background, 10.04 Refraction of Plane Wave using Huygens Principle, 10.05 Reflection of Plane Wave using Huygens Principle, 10.07 Red shift, Blue shift and Doppler Shift, 10.09 Coherent and Incoherent Addition of Waves: Constructive Interference, 10.10 Coherent and Incoherent Addition of Waves: Destructive Interference, 10.11 Conditions for Constructive and Destructive interference, 10.12 Interference of Light waves and Young’s Experiment, 10.13 Young’s Experiment, Positions of Maximum and Minimum Intensities and Fringe Width, 10.16 Diffraction of light due to Single Slit, 10.17 Resolving Power of Optical Instruments, 10.19 Polarisation by scattering and Reflection, 11.01 Dual Nature of Radiation and Matter: Historical Journey, 11.03 Photoelectric Effect: Concept and Experimental Discoveries, 11.04 Experimental Study of Photoelectric Effect, 11.05 Effect of Potential Difference on Photoelectric Current, 11.06 Effect of Frequency of Incident Radiation on Stopping Potential, 11.07 Photoelectric Effect and Wave Theory of Light, 11.08 Einstein’s Photoelectric Equation: Energy Quantum of Radiation, 11.09 Particle Nature of Light: The Photon, 12.02 Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom, 12.03 ⍺-Particle Trajectory and Electron Orbits, 12.05 Drawbacks of Rutherford’s Nuclear Model of Atom, 12.06 Postulates of Bohr’s Model of Hydrogen Atom, 12.07 Bohr’s Radius and Total Energy of an electron in Bohr’s Model of Hydrogen Atom, 12.09 Rydberg Constant and the line Spectra of Hydrogen Atom, 12.10 De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation and Limitations of Bohr’s Atomic Model, 13.01 Atomic Masses and Composition of Nucleus, 13.04 Mass-Energy Equivalence and Concept of Binding Energy, 13.07 Concept of Radioactivity and Law of Radioactive Decay, 13.09 Radioactive Decay : ⍺-decay, β-decay and -decay, 14 Semiconductor Electronics: Materials, Devices and Simple Circuits, 14.01 Semiconductors Electronics: Introduction, 14.05 Energy Band structure of Extrinsic Semiconductors, 14.07 Semiconductor Diode in Forward Bias, 14.08 Semiconductor Diode in Reverse Bias, 14.09 Application of Junction Diode – Half Wave Rectifier, 14.10 Application of Junction Diode – Full Wave Rectifier, 14.12 Optoelectronic Junction Devices: Photodiode and Solar Cell, 14.14 Concept and Structure of Bipolar Junction Transistor, 14.16 Common Emitter Transistor Characteristics, 14.18 Transistor as an Amplifier: Principle, 14.19 Transistor as an Amplifier – Common Emitter Configuration, 15.02 Basic Terminology Used In Electronic Communication system, 15.03 Bandwidth of Signal and Bandwidth of Transmission Medium, 15.04 Propagation of Electromagnetic Waves, 15.06 Types of Modulation and Concept of Amplitude Modulation, 15.07 Production and Detection of Amplitude Modulated Wave. (g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular? induced in the coil. A text Book of Physics. (g) When the permanent magnet is rotated in a vertical position, the field becomes parallel to rails. \begin{align*} \text {i.e. We can conclude that the electric field in the loop is not conservative because line integral of \(\vec E\) around a closed path is not zero. The function of the inductor depends upon the frequency of the current passing through it. 232, Block C-3, Janakpuri, New Delhi, Download the PDF Question Papers Free for off line practice and view the Solutions online. document.write('This conversation is already closed by Expert'); The rate at which energy is absorbed or released by inductor can be determined from the ordinary power formula. Calculate the average power loss due to Joule heating. Magnitude of flux of the flat coil, ϕ1 = B.A. ÎStart with loop rule ÎMultiply by i to get power equation ÎLet P L = power stored in inductor ÎIdentify energy stored in inductor ÎSimilar to capacitor: di iR L dt ε=+ L L dU di P Li dt dt == 1 2 L 2 ULidiLi==∫ iiRLi2 di dt ε=+ 2 C 2 q U C = Power produced = dissipated + stored Let I be the current at any instant of time so that di/dt is the rate of change of current. Induced Electric Fields and Energy Stored in an Inductor Induced Electric Fields. (d) What is the retarding force on the rod when K is closed? Share 7 ... For a DC RL circuit, the expression U = 1/2 L I 2 gives be energy stored in the inductor … Explain. Energy Stored in Inductor Establishing a current in the inductor requires work. Let i be the instantaneous current in the circuit then applying Kirchoff's voltage law, we get, The power supplied by the battery is given by. That is for higher frequency … due to change of magnetic field B. with distance (x) is,                     ε2 = dQdt ddtBA    A.dBdt     = A. dBdx.dxdt      = 144 × 10-4 × 10-1 × 8 × 10-2ε2 = 1152 × 10-7 Total e.m.f         ε1+ε2 = 144 × 10-7 + 1152 × 10-7         = 1296 × 10-7V        ε = 129.6 × 10-6V Resistance of the loop, R= 4.5 mΩTherefore, Induced current                       I= εR = 129.6 × 10-64.5 × 10-3             ≅ 2.9 × 10-2A. The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. Example : If the capacitance of a capacitor is 50 F charged to a potential of 100 V, Calculate the energy stored in it. 48 Energy of an Inductor ÎHow much energy is stored in an inductor when a current is flowing through it? Kathmandu: Surya Publication, 2003. If we neglect the small field outside the solenoid and take area vector \(\vec A\) to point in the same direction as be \(\vec B\)m then magnetic flux through the loop is given by, From Faraday's law, the induced emf is given by, \begin{align*} \epsilon &= -\frac {d\phi }{dt} = -\frac {d}{dt}(\mu_0\: nIA)\dots (i) \\ \text {or,} \: \epsilon &= -\mu _0nA\frac {dI}{dt} \dots (ii) \\ \end{align*}, If \(\epsilon \) be the induced emf, R be the total resistance of the loop, the induced current is, $$\text {i.e.}

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