Category: Project #3 groups

Section 6.3 The RLC Circuit

Group Members:

Imerson Memko, Nelson Feng Feng, Luyanda Dube, Aaron Libato, Timothy Khan, Keion Smith, Frank Garcia, Clifford Compere, Rafael Diaz, Joel Pena, Amel Lukovic, Freddy Perez

Lesson:

The RLC circuit section of the book consists of using Second Order Differential Equations to solve problems involving RLC circuits. RLC circuits are electrical circuit that consists of, as the name implies, Resistors, Inductors and Capacitors. The most common use of these circuits are in filters, which are used for pretty much used for everything that has electrical components inside it. RLC circuits are also used as voltage amplifiers. Namely, in car engines, they are able to generate very high voltage with a mere 12V, which then starts the engine.

RLC with a Current (I) Source

The RLC circuits in this chapter utilize a Current Source.

Current (I) = I(t) where t is time.

If I(t) > 0, then the current is flowing from the positive terminal of the source through the components then back to the ground of the same source.

If I(t) < 0, then the current is flowing from the ground terminal of the source through the components then back to the positive terminal of the same source.

I(t) = 0 means there is no current.

RLC components

Resistor: Resistance (R) represented by unit Ω and functions:
Voltage of Resistor

Inductor: Inductance (L) represented by unit H and functions:
Voltage of Inductor

Capacitor: Capacitance (C) represented by unit F and functions:
Capacitors store charge Q = Q(t) where

Voltage of Capacitor

RLC Source Differential Equation

where free oscillation is the homogeneous equation of

from which the characteristic equation can be found:

where the roots are

Cases:

Then the oscillation is underdamped. Therefore r1, r2 and the general solution will be:

Then the oscillation will be overdamped. Therefore the general solution will be:

Then the oscillation is critically damped. Therefore the general solution will be:

Examples of problems from our Group

Timothy Khan and Keion Smith Project 3 Part 1

Imerson Memko and Nelson Feng Feng Project 3 Part 1

Luyanda Dube and Aaron Libato Project 3 Part 1

Frank Garcia and Clifford Compere Project 3 Part 1

Rafael Diaz and Joel Pena Project 3 Part 1

Amel Lukovic and Freddy Perez Project 3 Part 1 and Video Lesson