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Show that $L I^{2} / 2$ has units of energy.

   Show that $L I^{2} / 2$ has units of energy.

University Physics

University Physics

Samuel J. Ling, Jeff… 2nd Edition

Chapter 14, Problem 10

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Solved by Expert Shahab Ullah

10/03/2020

Step 1

The unit of inductance (L) is henry (H), and the unit of current (I) is ampere (A). Since current is squared in the equation, the unit becomes ampere squared (A^2). Show more…

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Show that $L I^{2} / 2$ has units of energy.

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Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used to verify the consistency of equations by ensuring that both sides have the same fundamental units. In this context, it involves checking that the combination of inductance and current squared yields the same dimensional representation as energy. This method helps confirm that the mathematical expression adheres to the physical laws governing the dimensions.

Inductance

Inductance is a measure of a circuit element’s ability to store energy in its magnetic field when electric current flows through it. Its SI unit is the henry, which can be expressed in terms of fundamental units. Understanding the dimensions of inductance is essential when analyzing the units in an energy expression involving inductance.

Electric Current

Electric current, measured in amperes, represents the flow of electric charge within a circuit. In the energy expression, current appears squared, and analyzing its dimension is crucial because it contributes significantly to the overall dimensional balance needed to ensure that the expression has energy units.

Energy Units

Energy in the SI system is measured in joules, which have the dimensions of mass times length squared divided by time squared. By comparing the derived dimensions of the expression involving inductance and current to that of a joule, one can verify that the expression indeed corresponds to an energy quantity.

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