Elements of AC Circuits: The Series RLC Circuits - Lab Experiment 12 | PHYS 212, Lab Reports of Physics

Download Elements of AC Circuits: The Series RLC Circuits - Lab Experiment 12 | PHYS 212 and more Lab Reports Physics in PDF only on Docsity! Experiment 12: Elements of AC Circuits - The Series RLC circuit Purpose: To study the behavior of a resistor, capacitor and inductor in a series ac circuit. Prior to Lab: Sketch a phasor diagram for an ideal LRC circuit consisting of an 33 μF capacitor, a 70 mH inductor, and a 47 Ω resistor connected to a 5 v, 150 Hz source. Be sure you calculate XL and XC. Show these calculations. Theory: For a series RLC circuit, Kirchhoff’s rules demand that the current be a constant throughout. Furthermore, the potential differences across each element must combine to equal the source voltage. However, each element also has a unique phase relation between the potential difference and the current, so the potential differences must add according to the rules for combining phasors for the circuit. If we look at each element in turn we can investigate the individual behavior and then the collective behavior of the elements in the circuit. For example, the capacitor’s potential difference is determined by the charge on it, while the current is the rate of change of charge. This fact leads to a phase difference between current and voltage of 90o with the potential difference lagging the current by that phase angle. The effective potential difference across the capacitor VC equals the effective current I times the capacitive reactance XC. Figure 1. The apparatus wired and ready to read data. Note that the meter on the right is connected to the DMM Output of the Function Generator and is indicating the frequency output of the source. The meter on the left is set to read ac volts, and is reading the source voltage at this time. Procedure: In order to completely analyze the behavior of the circuit, we will measure the resistance R and five different potential differences at two different frequencies. We will also determine the resonant frequency of the circuit. Note: Before beginning the following procedure record the number of your circuit board so you will be able to use the same circuit board for next week’s AC Resonance Lab. 1/17/2007 1 1. BEFORE connecting wires to the circuit, use a DMM set on the 200 Ω range to measure the resistance between connection C and D in Fig. 2 or 3. The instrumental uncertainty for measuring resistance is 0.5% of the reading plus 1 digit. 2. Connect one DMM to the DVM Output of the function generator. Set this DMM to measure 20VDC. Note that the frequency measured is the product of the reading on this meter and the multiplier setting on the function generator. Connect the other DMM between A and D initially and set it to measure 20 VAC. 3. Connect the ac source to the circuit board using the 10 Ω resistor and the 100 μF capacitor. Set the function generator for 5.0 V at a frequency of 120 Hz. Note: Be certain the output is set for the sine wave function. Figure 2. Above is a diagram of the apparatus used in the experiment. C L r R A B C D Figure 3. Above is the schematic wiring diagram representing the apparatus and its source. Note that the inductor is not ideal, and we have represented any (power) loss in the circuit by a resistance, r, in series with the inductor. 4. Complete the measurements listed below for the frequency set in step 3 by connecting the probe wires of the DMM set to measure ACV to the connectors listed. Record this data in the first line of a table in your data notebook which looks like the sample below. When finished, change the frequency output of the function generator to 250 Hz and repeat the measurements to fill in the second line of the table in your data notebook. a. Vsource is measured by connecting the probes at A and D. b. VC is measured by connecting the probes at A and B. c. VLr is measured by connecting the probes at B and C. d. VLR is measured by connecting the probes at B and D. e. VR is measured by connecting the probes at C and D. f R Vsource VC VLr VLR VR 5. To measure the resonant frequency of the circuit connect the DMM used to measure ACV across points A and C to measure the combined voltage across the inductor and capacitor. 1/17/2007 2