Short- and Long-term Thinking
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Consider the circuit below, whose input I(t) is given by I_0\cos(\omega t):
1) Sinusoidal Steady State
When the system has reached steady state, find expressions for i_{\rm R}(t),
v_{\rm R}(t), i_{\rm L}(t), and v_{\rm L}(t). Enter your answers as
Python expressions below. Feel free to use mathematical constants like pi
or
e
or j
, or functions like sqrt
or ln
or atan
, or values from the circuit like
L
or R
or omega
or I_0
.
2) Transient Reminders
Let's now assume that the input current was instead given by I(t) = \begin{cases} 0 & \text{if}~t < 0\\ I_0\cos(\omega t) & \text{if}~t\geq 0 \end{cases}
This won't actually change the steady-state values from the first part (as t\to \infty), but let's think a little bit about what happens in the interim. Determine the following: