4. Consider the following circuit: Ss Its components all have the values: 1, y\'

Question

4. Consider the following circuit: Ss Its components all have the values: 1, y'= 12V, 2, R= 22k 3, C= 100011F 4. L = 30011H Assume that when you start all switches are open Close switches S1, S2, and S (a) What is the current through the circuit? Now, open switch S2 and close S. (b) What is the maximum voltage Vo across the capacitor C (c) How long does it take to charge the capacitor to ? What is the energy stored in the capacitor at this time? Open Ss and Ss when the voltage across the capacitor is Vo. Close S2 and connect Ss to the left pole (i.e. the one without the resistor) (d) What is the maximum current lo through the inductor L? (e) How long does it take for the current through the inductor to reach o What is the energy stored in the inductor at this time? Open Si and close Ss when the current through the inductor is Energy will begirn to flow back and forth between the inductor and capacitor in this LC circuit Like energy in a harmonic oscillator (f) What is the total electrical energy in the system? (g) Into which component will the energy move first? (h) LC circuits like this are used as timers because their frequency of oscillation is very precise. The frequency is given by wo (LC)-1. What is the oscillation frequency for the circuit?

Explanation / Answer

A) current i = V/R

= 12/22000 = 0.000545A= 0.545 mA

B) maximum voltage = 12V

C) 0.5V =V*(1-e^(-t/RC))

0.5 = 1-e^(-t/RC))

ln 0.5 = - t/RC

t = - RC ln 0.5

= - 22000*1000e-6 ln 0.5

= 22 ln 2

= 15.25 s

Energy stored = 0.5CV^2

= 0.5*0.001*12^2

= 0.072 J

D) maximum current i = 12/22000 = 0.000545A= 0.545 mA

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