Second Order Resistor Capacitor Inductor (RCL) Series Circuits

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{4}A_{41} Base Sequence = 12735 String Sequence = 12735 - 4 - 41 **

Expressions Of Pj Problems

Second Order Resistor Capacitor Inductor (RCL) Series Circuits

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

The circuit illustrated in figure 5.57 is a second order RCL circuit.

V_{s} = 12 V; C = 0.5 μF;

R_{1} = 31 kΩ; R_{2} = 22 kΩ

L = 0.9 mH.

The switch is closed at t = 0 after having been open for an extended period of time.

Determine:

(a) The current through the inductor after the circuit has returned to steady state.

(b) The voltage across the capacitor after the circuit has returned to steady state.

**The string**:

(a) S_{7}P_{4}A_{41} (Linear Motion - Current Flowing Into Passive Elements). The motion of current flow in an electric circuit can be viewed as piece-wise-linear (current flow into a device) or looped (current flow in a circuit branch or the entire circuit). In a series connection, the piece-wise-linear current and looped current are the same. In a parallel connection, they are not. The looped current is stringed as S_{7}P_{4}A_{42} (Curved Motion).

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

(a) Pj Prblem of Interest is of type *motion* (Linear Motion).

At steady state:

Current through inductor = i_{L}(∞); voltage across inductor = v_{L}(∞) = 0;

Current through capacitor = i_{C}(∞) = 0;
voltage across capacitor = v_{C}(∞)

Applying Kirchoff Voltage Law (KVL) to loop acdf we have:

V - R_{1}i_{L}(∞) - R_{2}i_{L}(∞) = 0 ---------(1)

So, 12 - (31 x 10^{3})i_{L}(∞) - (22 x 10^{3})i_{L}(∞) = 0;

So, i_{L}(∞) = 12/(53 x 10^{3}) = 226 x 10^{-6}) = 226 μA.

(b) Pj Problem of Interest is of type *force* (Force - Push).

At steady state, i_{C}(∞) = 0;

So, v_{C}(∞) = v_{R2}(∞)

v_{R2}(∞) = i_{L}(∞)R_{2} = (22 x 10 ^{3}) x (226 x 10 ^{-6}) = 4.97 V.

So, v_{C}(∞) = 4.97 V.

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

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

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