AC Circuits

While completing the experiment AC Circuits, make sure to keep the following guiding questions in mind :

•What is the relationship between the energy stored in the inductor and the energy stored in the capacitor when a power source is not present in the circuit? .

•How is energy dissipated in an AC circuit, within a resistor, within a capacitor, and within an inductor? .

•What are some of the applications of resonance in electrical and mechanical engineering? Is resonance always desirable? .

To complete the experiment you will need to:

1.Be prepared with a laboratory notebook to record your observations. .

2.Click the image to open the simulation experiment. .

3.Perform the experiment as described. .

4.Transfer your data and results from your laboratory notebook into the lab report template provided at the end of this experiment description. .

5.Submit your version of the laboratory experiment report. .

In your laboratory notebook, you will collect data, make observations, and ponder the questions posed within the lab instructions. Thus, the notebook should contain all the data collected and analysis performed, which will be invaluable to you as you write the results section of your laboratory report. Furthermore, the notebook should contain your observations and thoughts, which will allow you to address the questions posed, both for the discussion section in the laboratory report and in helping you to participate in the online discussion included in the module.

Part I –LC Circuit

· Start the simulation “Circuit Construction Kit (AC +DC)” (if you haven’t done so already) by clicking on the image below.

http://phet.colorado.edu/sims/circuit-construction-kit/circuit-construction-kit-ac_en.jnlp

· Build a circuit that has a battery, a capacitor and a switch.

· Right click on the capacitor and choose “change capacitance.” Use the slider to vary the capacitance.

http://phet.colorado.edu/sims/circuit-construction-kit/circuit-construction-kit-ac_en.jnlp

What behavior in the circuit do you observe when you close the switch? Do you observe any changes in the indications of charge stored on the plates of the capacitor? As the capacitance increases, what changes do you observe in the current and charge stored on the capacitor plates?

· Set the capacitor at 0.09 Farad. Carefully disconnect the battery from the circuit and build a new circuit with the charged capacitor (still at 0.09 Farad) and an inductor set at 11 Henrys—no battery.

· Bring the Current Chart to your circuit, and place the detector over a wire. You may have to adjust the +/- buttons for a good reading. Recall that the time for one cycle is called the period, and the frequency is equal to 1/period. In your laboratory notebook, record the values for capacitance, inductance, period, and frequency.

Use the definition of the resonant frequency from the module notes to calculate the resonate frequency of the AC circuit. How does this compare to the measured operating frequency of the LC circuit? Repeat this procedure for two other values of inductance and capacitance. Record the results in your laboratory notebook.

Part II – Phase Shift in an AC Circuit

· Build a circuit that has a capacitor and an AC source.

· Bring the Current Chart to your circuit, and place the detector over a wire. You may have to adjust the +/- buttons for a good reading.

· Bring the Voltage Chart to your circuit, and place the probes over the terminals of the capacitor. You may have to adjust the +/- buttons for a good reading.

Use the time scale on the horizontal scale of the Voltage Chart to measure the period of the voltage signal. Is the period for the potential the same as that measured for the current? Are the graphs on the two charts in phase? In other words do the peaks on the Current Chart and the Voltage Chart occur at the same time, or are they offset by some interval of time? Determine the value of this phase shift and whether current leads or trails voltage. (Note: If the period to complete 1 full cycle represents 360 degrees or 2π radians, then an offset between the peaks of ¼ of the full period represents 90 degrees or π/4 radians.)

· Replace the capacitor with an inductor. Determine the value of this phase shift, if any, and whether current leads or trails voltage. What is the relationship of this phase shift, if any, to that of the capacitor?

Part III – Resonance

An LC circuit initially charged will oscillate with energy flowing back and forth between the inductor and the capacitor. A circuit like this loses very little energy because neither inductors nor capacitors dissipate energy in the same manner as a resistor. If this circuit is driven by an external source at its natural frequency, energy will be added to the system during each cycle. In other words, the circuit will resonate, and exhibit oscillations with large currents.

· Construct an AC circuit with a capacitor, and inductor, and an AC current source.

· Set the capacitance to C = 0.09 Farad and the inductance to L = 11 Henrys.

· Right click the power source and set its frequency to a value that is not the resonant frequency of the circuit. Wait at least 2 minutes, and then write down your observations in your laboratory notebook.

· Pause the simulation, and reset the AC frequency so that it is equal to the resonant frequency of the circuit. Wait at least 2 minutes, and then describe your observations in your laboratory notebook. Be sure to point out any similarities or differences with the previous step.

· Add a resistor to the circuit with a very small resistance, R =0.01Ohms. Measure the peak current at frequencies (ƒ) equal to multiples of the resonance frequency. In particular, try frequencies equal to 0.5, 0.75, 0.9., 1.0, 1.1, 1.25, and 1.5 times the resonance frequency (ƒο).

Use your favorite spreadsheet program to plot peak current as a function of frequency on a scatter plot. Do not insert a trendline.