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Note: Items in red are measurements that must be made as you do the experiment.

Introduction In class, we learned about the behavior of circuits with capacitors, inductors, and resistors connected in series. Such a circuit is shown in Figure 1. Note that the actual inductor can be represented by a series combination of a pure inductance and a pure resistance connected in series.	Figure 1
The Undriven LRC Circuit When the capacitor is charged and connected to an inductor and resistor with no power supply attached, we know that the current in the circuit will oscillate. If there is no resistance, the frequency of oscillation is given by the expression:     Eq. 1 When a small resistance is added, the amplitude of the oscillation decays exponentially since energy is dissipated by the resistor. The frequency of oscillation remains very near the value given in Eq. 1. Select one of the capacitors available and connect it in series with the inductor provided as shown in Figure 1.  Do not include a resistor for this step.  The inductor has adequate internal resistance for our purposes. Record the values of L and C that you use. Inductance:  L = H Capacitance: C = F Use Eq. 1 to calculate the frequency of oscillation: Oscillation frequency:   f0  =  Hz In order to charge the capacitor and let the circuit oscillate freely, we can simply apply a square wave to the circuit. Set the signal generator to square-wave mode and select a frequency that is well below the expected natural frequency of the circuit. Connect the oscilloscope leads across the capacitor to observe the capacitor voltage as a function of time. The capacitor voltage is proportional to the charge on the capacitor (Q=CV) and oscillates at the same frequency as the current in the circuit. (i=dQ/dt).  You will need to know horizontal time scale of the oscilloscope screen, which is set with the “Horizontal Sweep” dial, to measure the oscillation period, T. Recall that the frequency is f=1/T. Measured frequency:  f = Hz. Estimate the time constant for the damping of the oscillations. This is the time required for the amplitude (the crests) to drop to 37% of their original value. Note that this should be equal to 2L/R. Estimated damping constant:   s.
The Driven LRC Circuit When a driving force is applied to the circuit, the circuit will oscillate at the same frequency as the driving force; however, the amplitude of the oscillations depends on the driving frequency. When the frequency is low, the capacitor has more time to charge and offers a large effective resistance to the flow of current. When the frequency is high, the inductor produces a large induced EMF, which again offers a large effective resistance. The total impedance of the system is minimum at the natural frequency of the system, given by Eq.1. Select one of the available resistors and add it to your circuit as in Figure 1.  Switch the signal generator to sine-wave mode. Using the appropriate combination of the push=button and dial settings, set the frequency of the signal generator to the natural oscillation frequency you measured above. Connect your oscilloscope leads to either side of the resistor and view the signal on the oscilloscope. Since V=IR for the resistor, the resistor voltage is proportional to the current. Adjust the of the resistor voltage 1 V. (Remember that amplitude is 0 to max; however, it may be easier to set min to max to 2 V.)  Now try adjusting the frequency of the signal generator. Find the resonant frequency, the frequency where the current is largest. Record this frequency and VR at resonance. Resonant frequency: fres = Hz. VR at resonance = V. With the circuit at resonance, measure the voltages across the signal generator, the capacitor, and the inductor individually. EMF at resonance = V. (Voltage across the signal generator.) VL at resonance = V. VC at resonance = V. Note that at resonance, VR should equal the EMF, and VL should equal  VC  as long as the resistance of the inductor can be neglected. This should be clear by considering the phasor diagram of these voltages at resonance. Figure 2