Question

14. Consider a parallel RLC circuit (shown below) which we have not discussed in class. This can be most easily analyzed by writing the KCL equation for the upper node, assuming the lower node has 0 potential. Assume the capacitor is initially charged to 100 Volts and that the switch is closed at t=0. a) Find a differential equation whose solution is the voltage of the upper node. Remember that the capacitor is discharging, so $i(t) = -\frac{dq}{dt}$ b) If the circuit elements have the same values of in problem 13, is the circuit over, under or critically damped? c) What are the initial conditions for the Voltage and the derivative of the Voltage at t=0? 15. The switch in the circuit below is closed at t=0. Find the current in the inductor as a function of time.

          14. Consider a parallel RLC circuit (shown below) which we have not discussed in class. This can be most easily analyzed by writing the KCL equation for the upper node, assuming the lower node has 0 potential. Assume the capacitor is initially charged to 100 Volts and that the switch is closed at t=0.
a) Find a differential equation whose solution is the voltage of the upper node. Remember that the capacitor is discharging, so $i(t) = -\frac{dq}{dt}$
b) If the circuit elements have the same values of in problem 13, is the circuit over, under or critically damped?
c) What are the initial conditions for the Voltage and the derivative of the Voltage at t=0?
15. The switch in the circuit below is closed at t=0. Find the current in the inductor as a function of time.

14. Consider a parallel RLC circuit (shown below) which we have not discussed in class. This can be most easily analyzed by writing the KCL equation for the upper node, assuming the lower node has 0 potential. Assume the capacitor is initially charged to 100 Volts and that the switch is closed at t=0.
a) Find a differential equation whose solution is the voltage of the upper node. Remember that the capacitor is discharging, so i(t) = -(dq)/(dt)
b) If the circuit elements have the same values of in problem 13, is the circuit over, under or critically damped?
c) What are the initial conditions for the Voltage and the derivative of the Voltage at t=0?
15. The switch in the circuit below is closed at t=0. Find the current in the inductor as a function of time.

Added by Domingo U.

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