RCL Circuits Frequency: 20.0 kHzAmplitude: 6.0 VDuty Cycle: 50%Time/Div each cycle: 0.1 micro sec.Volts/Div: 0.1 VR_inductor = 5.8 ohmsL = 8.2 mHC = 330 micro F

Part A. Free Oscillations: For this part we will be using a square wave. In the absence of any resistance, an LC circuit will be oscillating with no damping. The current will be constantly changing direction as the capacitor charges first then the induced emf in the inductor forces the electrons to move in the other direction. The resistance of the circuit (including the resistance of the inductor) slows the oscillation. VS During the capacitor discharge: (1) L is the inductance of the inductor, it is measured in Henry. The solution to the differential equation (1) is: (2) Notice that the solution is a combination of an exponential decay and a sinusoidal part. R is the resistance of the generator plus the resistance of the inductor. The exponential curve that connects the maxima of the oscillating charge is the envelope function and will help us to get the time constant of RCL circuit: 1. Using Excel and the same method used in RC circuit, get time constant from the maxima of the curve on the oscilloscope. 2. Compare to the value of the time constant from equation (3) 3. Measure the frequency of oscillations from the graph on the oscilloscope. 4. Calculate the value of the frequency given above. Compare 5. Is this frequency equal to the frequency from the function generator? Why? Part B: Critical Damping: There is a specific resistance for which the circuit just stops oscillating. We talk then about critical damping. 1. Find its value? 2. What would we do to measure it? Part C: Driven/ forced Oscillations: Using a sine wave What do you think will happen when the Vs is switched to a sine wave? Why is this called driven oscillations or forced oscillations