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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.