LC Matching

The questions below are due on Monday November 18, 2024; 10:00:00 PM.
 
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Consider the following circuit:

Before time t=0, the switch is open, and it has been open long enough that the circuit has reached equilibrium (no current through the inductor and no voltage across the capacitor). At time t=0, the switch is closed.

Consider the following 6 graphs measuring either currents or voltages in the circuit, and use them to answer the following questions about the circuit. The units for the vertical axies of each graph are either Amps or Volts, depending on whether it is depicting a current or a voltage.

Note also that the range of values shown on the vertical axis is differs from plot to plot; pay close attention to those!

What is the natural frequency \omega_o of this circuit, in units of radians per second?

Which graphs represent v_L, v_C, i_L, and i_C, respectively? Enter your answer as a sequence of numbers in order, i.e., 1111 if you think the appropriate graph for each value is graph 1. You can also separate the numbers with commas and/or spaces if you want.

What is the value of V_o, in units of Volts?
 
V_o (in Volts) =~

What is the value of C, in units of Farads?
 
C (in Farads) =~

What is the value of L, in units of Henries?
 
L (in Henries) =~