Survey

Transcript

PHYS-2100 Introduction to Methods of Theoretical Physics Fall 1998 Homework Assignment Due Thursday, Sept. 3 1) Consider the following circuit, in which a current i flows through a resistor R and an inductor L to ground, for times t > 0 . For earlier times, the voltage V 0 = 0 so no current flows: V 0(t > 0) R V(t) i L a) Show that the current obeys the following equation: di V 0 = iR + L ----dt b) Show that, for any value of the constant K, a solution to this equation is given by V – ( R ⁄ L )t i ( t ) = -----0- + K e R c) The current is 0 at time t = 0 . Use this to determine the constant K. d) Find an expression for the voltage V(t). Does this give you the values you expect at t = 0 and for t → ∞ ? Briefly explain your reasoning.