The coefficient of self-induction L (in henrys), the energy...

The coefficient of self-induction $L$ (in henrys), the energy $P$ stored in an electronic circuit (in joules), and the current $I($ in amps) are related by this formula.
$$
I=\sqrt{\frac{2 P}{L}}
$$
(a) Find $I$ if $P=120$ and $L=80$
(b) Find $I$ if $P=100$ and $L=40$

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Key Concepts

Self-Inductance

Self-inductance is a property of a circuit element, particularly an inductor, that quantifies its ability to resist changes in current by inducing an electromotive force in itself. It is measured in henries and is fundamental in analyzing transient behaviors in electrical circuits.

Magnetic Energy Storage

The energy stored in the magnetic field of an inductor is described by the equation E = 1/2 L I². This relationship links the self-inductance with the current flowing through the inductor, demonstrating how energy is accumulated and subsequently can be released in electromagnetic systems.

Algebraic Manipulation of Formulas

Rearranging formulas to solve for a desired variable, such as isolating the current from the energy equation, is a key skill in physics and engineering. It involves techniques like taking square roots and substituting known values to find unknown quantities.

Dimensional Analysis

Keeping track of and correctly handling units—henries for self-inductance, joules for energy, and amperes for current—is essential to ensure that the mathematical expressions are physically meaningful and that calculations yield correct results.

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