Double-Exponential LR Circuit

Abstract

Simple LR and RC circuits are familiar to generations of physics students as examples of single-exponential growth and decay in the relevant voltages, currents, and charges. An element of novelty can be introduced by connecting two (instead of one) LR coils in parallel with a battery. The resulting circuit can still be treated using little more than the basic tools (Kirchhoff s rules plus a trial exponential solution) employed in the standard LR analysis. But the solution is now a double exponential, as can be verified by constructing such a circuit. Consider a circuit consisting of two inductors L1 and L2, one battery epsilon, one switch S, and three resistors R1 through R3. Assume the currents in the circuit have reached their steady-state values with switch S open. The switch is then closed at t = 0. The problem is to find the subsequent currents in the circuit as a function of time.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2005
Accession Number
ADA574982

Entities

People

  • Carl E. Mungan

Organizations

  • United States Naval Academy

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DTIC Thesaurus Topics

  • Amplitude
  • Circuits
  • Contrast
  • Differential Equations
  • Equations
  • Equivalent Circuits
  • First Order Circuits
  • Inductors
  • Information Operations
  • Instructors
  • Linear Differential Equations
  • Power Supplies
  • Resistance
  • Resistors
  • Steady State
  • United States Naval Academy
  • Variable Resistors

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Electrical Engineering