Energy Stored in an Inductor, calculating inductance

In summary, an inductor is an electronic component that stores energy in the form of a magnetic field and is commonly used in circuits to control electricity flow. Its inductance can be calculated using the formula L = N^2 * µ * A / l, where N is the number of turns in the coil, µ is the permeability of the core material, A is the cross-sectional area of the coil, and l is the length of the coil. The unit of inductance is the henry (H) and the energy stored in an inductor is directly proportional to its inductance, as shown by the formula E = 1/2 * L * I^2. Factors that affect the inductance of
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Homework Statement



The electric-power industry is interested in finding a way to store electric energy during times of low demand for use during peak-demand times. One way of achieving this goal is to use large inductors. What inductance L would be needed to store energy 3.0 (kilowatt-hours) in a coil carrying current I= 300 A?

Homework Equations



U = 1/2 LI^2
L = 2E / I^2

3.0 kWh = 1.08*10^7

The Attempt at a Solution



2(1.08 * 10^7) / 900 A^2 = 24,000 H
 
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##300^2 \ne 900##
 

Related to Energy Stored in an Inductor, calculating inductance

What is an inductor?

An inductor is an electronic component that is used to store energy in the form of a magnetic field. It is typically made of a coil of wire and is often used in circuits to control the flow of electricity.

How is inductance calculated?

The inductance of an inductor can be calculated using the formula L = N^2 * µ * A / l, where N is the number of turns in the coil, µ is the permeability of the core material, A is the cross-sectional area of the coil, and l is the length of the coil.

What is the unit of inductance?

The unit of inductance is the henry (H), named after the scientist Joseph Henry. It is equivalent to one volt-second per ampere (V-s/A).

How does the energy stored in an inductor relate to its inductance?

The energy stored in an inductor is directly proportional to its inductance, meaning that the higher the inductance, the more energy can be stored in the inductor. This relationship is described by the formula E = 1/2 * L * I^2, where E is the energy stored, L is the inductance, and I is the current flowing through the inductor.

What factors affect the inductance of an inductor?

The inductance of an inductor is affected by various factors such as the number of turns in the coil, the core material used, the cross-sectional area and length of the coil, and the presence of any nearby magnetic fields or conductive materials.

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