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Ch 30: Inductance
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 30: InductanceProblem 20b
Chapter 30, Problem 20b

It has been proposed to use large inductors as energy storage devices. If the amount of energy calculated in part is stored in an inductor in which the current is 80.0 A, what is the inductance?

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Start by recalling the formula for the energy stored in an inductor: \( E = \frac{1}{2} L I^2 \), where \( E \) is the energy, \( L \) is the inductance, and \( I \) is the current.
Rearrange the formula to solve for inductance \( L \): \( L = \frac{2E}{I^2} \).
Identify the values given in the problem: the current \( I = 80.0 \) A and the energy \( E \) which was calculated in part (a).
Substitute the known values into the rearranged formula: \( L = \frac{2E}{(80.0)^2} \).
Ensure units are consistent and calculate \( L \) using the substituted values to find the inductance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Stored in an Inductor

The energy stored in an inductor is given by the formula E = (1/2)LI^2, where E is the energy, L is the inductance, and I is the current. This relationship shows how energy is related to the inductance and the square of the current flowing through the inductor.
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Inductance

Inductance is a property of an electrical conductor that quantifies its ability to store energy in a magnetic field when current flows through it. It is measured in henries (H) and depends on factors like the coil's geometry and the core material. Inductance determines how much energy can be stored for a given current.
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Current

Current, measured in amperes (A), is the flow of electric charge through a conductor. In the context of inductors, the current is crucial because the energy stored is proportional to the square of the current. A higher current results in more energy stored, assuming the inductance remains constant.
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Related Practice
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