Parallel RLC Circuit - Energy Stored In Inductor

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 3 - 32 **

Expressions Of Pj Problems

Parallel RLC Circuit - Energy Stored In Inductor

Math

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Figure 5.58 is the RCL circuit for the given circuit elements:

voltage source, V_{s1} = 15 V; R_{s1} = 130 kΩ;

inductance, L = 17 mH; R_{1} = 1.1 kΩ

Capacitance, C = 0.35 μF; R_{2} = 700 Ω R_{s2} = 290 kΩ;

voltage source V_{s2} = 9 V;

Assume DC steady state conditions exist for t < 0 and as t approaches ∞

If switch is open at t = 0; Determine:

(a) Energy stored in inductor at t = 0^{+}, just after the switch S is open.

(b) Energy stored in inductor as t → ∞

**The strings**:

(a) and (b): S_{7}P_{3}A_{32} (Force - Push)
**The math**:

Pj Problem of Interest is of type *force*. Work and energy problems are *force problems*.

(a) DC steady state conditions exist for t < 0

So, inductor voltage, v_{L}(0^{-}) = 0.

And capacitor current, i_{C}(0^{-}) = 0.

So, i_{L}(0^{-}) = i_{s1}(0^{-}) + i_{s2}(0^{-})

So, i_{L}(0^{-}) = v_{s1}/R_{s1} + v_{s2}/R_{s2}

So, i_{L}(0^{-}) = 15/130 + 9/290 = 0.11538 + 0.03103 = 146.4 mA.

i_{L}(0^{-}) = i_{L}(0^{+}) (for continuity).

So, i_{L}(0^{+}) = 146.4 mA

Energy stored in inductor = (1/2)L(i_{L})^{2}

So, Energy in inductor = (1/2) x (17 x 10^{-3}) x (146.4 x 10^{-3})^{2} = 0.182 mJ.

(b)steady state conditions exist for t → ∞

At this time switch S has been open for a long time.

So, i_{L}(∞) = v_{s2}/R_{s2} = 9/290 = 0.03103 = 31.03 mA.

So, Energy in inductor = (1/2) x (17 x 10^{-3}) x (31.03 x 10^{-3})^{2} = 0 mJ.

Energy stored in a capacitor = (1/2)C(i_{c})^{2}

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings