﻿ Second Order Resistor Capacitor Inductor Series Circuit - RCL Circuits

Second Order Resistor Capacitor Inductor (RCL) Series Circuits

Strings (SiPjAjk) = S7P4A41     Base Sequence = 12735     String Sequence = 12735 - 4 - 41

Expressions Of Pj Problems
Second Order Resistor Capacitor Inductor (RCL) Series Circuits
Math

The circuit illustrated in figure 5.57 is a second order RCL circuit.
Vs = 12 V; C = 0.5 μF;
R1 = 31 kΩ; R2 = 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) S7P4A41 (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 S7P4A42 (Curved Motion).
(b) S7P3A32 (Force - Push).
The math:

(a) Pj Prblem of Interest is of type motion (Linear Motion).
Current through inductor = iL(∞); voltage across inductor = vL(∞) = 0;
Current through capacitor = iC(∞) = 0; voltage across capacitor = vC(∞)
Applying Kirchoff Voltage Law (KVL) to loop acdf we have:
V - R1iL(∞) - R2iL(∞) = 0 ---------(1)
So, 12 - (31 x 103)iL(∞) - (22 x 103)iL(∞) = 0;
So, iL(∞) = 12/(53 x 103) = 226 x 10-6) = 226 μA.
(b) Pj Problem of Interest is of type force (Force - Push).
At steady state, iC(∞) = 0;
So, vC(∞) = vR2(∞)
vR2(∞) = iL(∞)R2 = (22 x 10 3) x (226 x 10 -6) = 4.97 V.
So, vC(∞) = 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

Blessed are they that have not seen, and yet have believed. John 20:29