Energy Stored In An Inductor
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Energy Stored In An Inductor
Electromagnetic Induction of Class 12
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The battery that establishes the current in an inductor has to do work against the opposing induced emf. The energy supplied by the battery is stored in the inductor. Let i be the instantaneous current in the circuit then applying Kirchoff's voltage law, we get E = iR + Ldi/dt The power supplied by the battery is given by P = Ei = i2R + Li di/dt |
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where i2R is the power dissipated in the resistor and the last term represents the rate at which energy is being supplied to the inductor.
The total energy stored when the current rises from O to I is found by integration.
U =
(4.16)
The self inductance of a solenoid is
L = µ0n2Al
Since B = µ0nI, therefore,
L =
Thus, energy stored is
U =
Since Al is the volume of the solenoid the energy per unit volume stored in the solenoid is
u =
(4.17)
This is the energy density of a magnetic field in free space.
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Example: 4.11 A coaxial cable consists of internal solid inductor of radius a and external thin walled conducting tube of radius b. Find the inductance of a unit length of the cable, considering that the current distribution over the cross-section of the internal conductor is uniform. The permeability is equal to unity everywhere |
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Solution
The magnetic field inside the coaxial cable is given by
B1 =
for r ≤ a
B2 =
for a ≤ r ≤ b
B3 = 0for r > b
The magnetic energy stored in the cable per unit length is
U =
or U =
or U =
Using equation (4.16) we have
U =
L =
Frequently Asked Question (FAQs)
Q1. How do energy stored in an inductor?
Ans. Let assume we have an electrical circuit containing a power source and a solenoid for inductance L, we can write the magnetic field number, E, stored in the inductor as E = 1/2 x L x I², where I is the current flowing through the wire.
Q2. How much energy is stored in an inductor in a steady-state?
Ans. If the current flowing in the inductor does not change as in the DC circuit, then there will be no change in the stored energy, such as P = Li (di / dt) = 0.
Q3. What is the inductor formula?
Ans. We know that the voltage across an inductor is given by the equation. V = L di / dt. We can write, v AB = L Total x dlt / dt. V AB = L Total x d (I 1 + I 2 + I 3 ) / dt.
Q4. What is the energy stored in the capacitor?
Ans. Electrostatic potential energy gets stored in the capacitor. It is then related to the charge and voltage between the capacitor plates.
Q5. What is the unit of inductor?
Ans. The SI unit of inductance is Henry, abbreviated as 'H'. It is defined as the measure of electric current changes at one ampere per second, resulting in an electromotive force of one volt across the inductor.
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