An RLC circuit consists of a 25 mH inductor, a 0.001 µF capacitor and a variable

Question

An RLC circuit consists of a 25 mH inductor, a 0.001 µF capacitor and a variable resistor connected in series.

The initial charge on the capacitor at t = 0 when the switch is closed is 1 mC.

What is the critical resistance Rc for this circuit (the resistance that makes the oscillation of charge critically damped)?

Also, generate three plots of the charge on the capacitor vs. time:

1.) Q(t) from t = 0 to t = 1 ms for R = 0.01 x Rc

2.) Q(t) from t = 0 to t = 1 ms for R = 0.1 x Rc

3.) Q(t) from t = 0 to t = 1 ms for R = Rc from t = 0

Explanation / Answer

Rc=2*(L/C)=2*(0.025/(1E-9))10 k==>Q(t)=Qo*(1+*t)*e-*t

is the damping coefficient==> is the damped frequency of oscillation

=R/(2*L)=0.01*10,000/(2*0.025)2,000 Neper freq.

=1/(L*C)=1/(0.025*1E-9)200,000 rad/s

1) Q(0.001)=0.001*[1+2,000*0.001]*e-200,000*0.0014.15 E-90 C

2) 2.91 E-89 C

3) 2.78 E-88 C

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