**Lab 221: LC Circuits**

**Physics 2**

**Objective:**

To examine LC circuit and resonance frequency

**Theoretical Background**

Energy can be stored either as potential energy or kinetic energy

In a LC circuit electrical potential energy is attributed to charges at rest (gathered in a capacitor)

(1) U_{E}= , where q is a charge on a capacitor with capacitance, C

And kinetic energy is attributed to moving charges (current) and is equal to:

(2) K = LI^{2}, where I is a current through inductor with inductance, L

At some conditions total energy, U of a system may continuously keep swapping between one kind of energy and the other - possibly creating oscillations (like with a pendulum)

In case the system is isolated and doesn’t lose (acquire) any energy - the energy is conserved

For an LC circuit consisting only inductor L and capacitor C, we have:

(3) U = + LI^{2} = constant

The derivative of U is then:(4) = ()()+(LI)(= 0

Since I = ,

(5) L+ = 0 And the solution is: oscillation

I(t) = I_{max}sin(ωt+Φ), where ω^{2} =

In this laboratory, a simple electric oscillator is constructed using an inductor L and a capacitor C connected in series

The capacitor is initially charged to 5 V then discharged through the inductor

In this experiment, there are two capacitors (47 μF and 100 μF) and two inductors (23 mH current loop and 8.5 mH solenoid) that will be used in various combinations to create LC circuits oscillating at various frequencies

**Procedure:**

**Part I:**

**Using the LCR meter, measure the exact values of inductance and capacitance for the two inductors and capacitors. Also measure the resistance of the inductors. Record all the measured values in the Data Table.****Calculate the expected resonant frequency for the four combinations of inductance and capacitance to be used in this experiment using equation (7)**

**Part II:**

**Use the computer as a digital oscilloscope.****Log in to the lab computer using your UCID and password.****Connect the USB cable of the 850 Universal Interface to a USB port on the computer.****Connect the AC adapter power cord to an electrical outlet under the lab table.****Press the power push button on the left front corner of the interface. The green LED indicator below the power push button should light up.****Connect the Voltage probe to the Analog INput A on the 850 interface and construct LC circuit as shown in Figure 3.****Make sure that the toggle switch is positioned toward “A”.****Open “Lab 221 LC Circuit” file in “Physics 121A Lab Experiments” folder on Desktop.****Go to the Measurement” page in the software and open “SIgnal Generator” on “Tools” at the left side of the screen.****Click “On” button on the 850 Output 1 screen to charge the capacitor. Make sure that the capacitor is fully charged by measuring the voltage across the capacitor using the multimeter.****After clicking “Record” button, turn the switch from A to B positon which is toward the inductor. The software starts to record the data.****When the recording is done, click “Off” button on the 850 Output 1 screen.****Go to the Analysis page to find out the frequency of the LC circuit.****Using the “Select visible data” tool, select the data that you just measured.****Using the “Highlight range of points” tool, select the range of the data.****Click “Select curve fits to be displayed” tool on the top of the graph and select “Dampled Sine” function to do the curve fitting.****Compare the results of the best fit with you theoretical calculations (Equation 7).****Calculate f’ for the used combinations of Ls and Cs to see if it changes your results for this capacitor and inductor.****Repeat for the other combinations of inductance and capacitance. Check the calculation for f’ in each case.**

**Discussion:**

The capacitor you use in the experiment is an electrolytic capacitor. It should have electrode marked (+) and charge only with a positive charge

- What could have happened if you charge the electrolytic capacitor in reverse direction?

Charging an electrolytic capacitor in the reverse direction could lead to the destruction of the

dielectric and loss of capacitor functionality. Resulting heat and pressure buildup pose a hazard.

- Do you think the electrolytic capacitor is right for this experiment? Why or why not?

The electrolytic capacitor is right for the experiment because of their large capacitance and

consequential ability to store large quantities of energy. The storage and movement of this energy

between capacitor and inductor are the main foci of the experiment.

- What makes the sine wave amplitude decreasing so fast that you have few oscillations only?

The sine wave amplitude decreases so fast because of the size of the damping constant, B = R/2L. The w’ and f’ take this into account, and damped current decreases proportionally to e^{-Bt}.

- Do you understand that you have just emitted radio wave with frequency f? If you tune a radio to this frequency would you be able to hear it? Why or why not?

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