1 / 34

Understanding First-Order RL and RC Circuits in Electrical Engineering

This document explores the relationship between differential equations and electrical engineering, specifically focusing on first-order RL and RC circuits. It covers fundamental concepts such as voltage, current, resistors, inductors, and capacitors. The objective is to derive the first-order differential equations related to these circuits, estimate solutions, and understand their graphical representation. Key analytical techniques, such as Ohm's Law and Kirchhoff's Laws, are also discussed to aid in the comprehension of circuit behavior in natural and step responses.

uriah-cruz
Télécharger la présentation

Understanding First-Order RL and RC Circuits in Electrical Engineering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. First-Order RL&RC Circuits DONE BY AL-AHMED, UTHMAN SULTAN ELECTRICAL ENGINEERING DEPARTMENT

  2. Objective:- • to show you the relationship between MATH 202 and the electrical engineering major. • To obtain the first order differential equation • To estimate the solution of RC or RL circuit. • To understand the physical meaning of the obtained differential equation. • To show you graphical solution.

  3. Background • In the begging I would like to introduce some terminology related to electrical devices:- Voltage sorce, current source, inductor ,resistor and capacitor

  4. Voltage • Defination :- is the energy per unit charge created by the separation (positive and negative charge). • Mathematical expression :-

  5. Cont. voltage • Circuit symbol:- Where V=the voltage in (volts) W=the energy in (joules) q= the charge in (coulombs)

  6. Current • DEFINATION the rate of charge flow. • Mathematical expression

  7. Cont. current • Where i= the current in (amperes) q= charge in (coulombs) t=the time in (seconds) Circuit symbol:-

  8. Resistor • Defination:- is the circuit element which used to model the behavior of resistance phenomena. Resistance phenomena ( is the capacity of materials to impede the flow of current or more specifically , the flow of electric charge)

  9. Cont. resistor • Circuit symbol:-

  10. Inductor • is an electrical component that oppose any change in electrical current and it is composed of coil of wire wound around a supporting core whose material may be magnetic or nonmagnetic. • The behavior of inductor is based in phenomena associated with magnetic field (( source of magnetic field is charge in motion, or current.

  11. Cont. inductor • Where V= voltage between inductor in (volt) L= inductor in (henery) = rate of change of current flow in amper = rate of change of time in second

  12. cont. inductor • Circuit symbol:-

  13. Capacitor • DEFINATION:- • is an electrical component that consists of two conductors separated by an insulator or dielectric material. His job is to sore energy like battery. • The behavior of inductor is based in phenomena associated with electric field ( the source of electric field is separation of charge or voltage.

  14. Cont. capacitor • Mathematical relation • Where i= current that in capacitor in (ampere) C= capacitance in (farad) = rated of change of voltage. = rate of change of time in second .

  15. Cont. capacitor • Circuit symbol:-

  16. The Basic Analytical Techniques • (1) OHM’s Law

  17. KVL (2) Kirchhoff’s law 1 The algebraic sum of all voltage around any closed path in circuit equal to zero

  18. KCL • Kirchhoff’s law 2 The algebraic sum of all current at any node in a circuit equal to zero

  19. Response of First-Order RL and RC Circuits My objective here extend to two main parts • Natural Response • Step Response

  20. Natural Response

  21. Step Response

  22. The Natural Response Of An RL Circuit Required • Find i(t) by obtain the D.E? • Solve the D.E.

  23. Solution (1)We use KVL to obtain an expression involving i,R,L (2) summing the voltage around the closed loop gives

  24. Remark about D.E • this equation a first order ordinary D.E. • it contains terms involving the ordinary derivative (). • The highest order derivative is 1 • L & R constant (they are not function of either dependent variable i or independent variable t) • We can say ,this equation is ordinary D.E with constant coefficients

  25. Solving the D.E • To solve the D.E we divide by L

  26. We transpose the term involving i to right hand side

  27. Multiply both sides by dt

  28. We divide by I

  29. We integrate both side

  30. the final answer is

  31. The Natural Response Of An RC Circuit • IS ANALOGOUS TO RL

  32. D.E. OF RC

  33. FINAL ANSWER

  34. Thank You For Attention

More Related