AC introduced to circuits and see how they

AC Circuits I & II LabBy Will AxonPhysics 231 Section 0095 December 2017Introduction            AC circuits were first introduced by Nikola Tesla. The purpose to this lab was to be introduced to circuits and see how they can be used in several different applications. The alternating current circuits of this experiment contained resistors and capacitors. This experiment is conducted using a simple alternating current (AC) circuit containing several resistors and capacitors.

If done correctly we should be able to see and measure how current flows through a circuit. For the AC circuit with the resistor we use Ohm’s Law,VR=ISRto show the voltage of the AC circuit can be calculated. The voltage across the resistor with respect to time can be depicted by the equationVR =VRM cos ?tFor the AC circuit with the capacitor, the equation VC =VCM cos(?t +?)is used to calculate the voltage across the capacitor with respect to time.

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ProcedureThe apparatus for this experiment contains a Pasco CI-6512 RLC circuit board containing a resistor and capacitor.  After the circuit board is set up for the capacitor the DataStudio Program is set up on the computer in order to record the data produced during the experiment.  After the data is recorded, the smart tool cursor is used in DataStudio to find the exact values of the peaks of the current and voltage.  Using the measured time and the period of oscillation the phase difference can be found.  This procedure was repeated for the resistor in the AC circuit.  Frequency, Im, Vcm, Vrm  , Angular Frequency, Time, Phase Angles, Vcm/Time and Vrm/Time were all recorded and shown below along with their graphs. Results R= 33 C= 3.30E-04   Frequency Im Vcm Angular Frequency Im/Vcm Time (Current) Time (Voltage) Phase Angles (radians) 9.

950249 0.068 0.318 62.51925679 0.

213836 0.1971 0.2215 1.525469866 20 0.093 2.

288 125.6637061 0.040647 0.097 0.1087 1.

470265362 30 0.1053 1.719 188.4955592 0.061257 0.

0331 0.041 1.489114918 40 0.11 1.

368 251.3274123 0.080409 0.0246 0.0305 1.482831732 50 0.113 1.

13 314.1592654 0.1 0.0197 0.0245 1.507964474 60 0.

114 0.96 376.9911184 0.11875 0.

0161 0.0201 1.507964474 70 0.116 0.833 439.

8229715 0.139256 0.0142 0.0176 1.495398103 80 0.116 0.734 502.

6548246 0.158038 0.0123 0.0154 1.

558229956 90 0.116 0.664 565.4866776 0.

174699 0.0109 0.0135 1.470265362 100 0.

117 0.593 628.3185307 0.

197302 0.0199 0.0223 1.507964474 110 0.

117 0.537 691.1503838 0.217877 0.0181 0.0202 1.451415806 120 0.

116 0.494 753.9822369 0.234818 0.0164 0.0184 1.

507964474 130 0.117 0.466 816.8140899 0.251073 0.0154 0.0172 1.

470265362 140 0.117 0.424 879.645943 0.275943 0.

0142 0.0159 1.495398103 150 0.

119 0.41 942.4777961 0.

290244 0.0133 0.0148 1.413716694       Frequency Im Vrm Angular Frequency Vrm/Im Time (Current) Time (Voltage) Phase Angles (radians) 10 0.

12 3.969 62.83185307 33.075 0.0242 0.

0242 0 20 0.12 3.969 125.6637061 33.075 0.0617 0.0617 0 30 0.

12 3.969 188.4955592 33.

075 0.0743 0.0743 0 40 0.12 3.969 251.

3274123 33.075 0.0559 0.0558 0 50 0.12 3.969 314.

1592654 33.075 0.0445 0.0444 0 60 0.12 3.969 376.9911184 33.075 0.

0537 0.0536 0 70 0.12 3.969 439.8229715 33.

075 0.0457 0.0458 0 80 0.12 3.969 502.

6548246 33.075 0.0274 0.0274 0 90 0.

12 3.969 565.4866776 33.075 0.0246 0.

0247 0 100 0.12 3.969 628.3185307 33.

075 0.0322 0.0321 0 110 0.12 3.969 691.1503838 33.

075 0.0293 0.0293 0 120 0.12 3.969 753.9822369 33.

075 0.0351 0.0352 0 130 0.

12 3.969 816.8140899 33.075 0.

0169 0.0168 0 140 0.12 3.969 879.645943 33.

075 0.0159 0.016 0 150 0.12 3.969 942.

4777961 33.075 0.0148 0.0148 0     %diff Im/Vcm 9.090909 Im/Vrm 0              The results in this experiment were very good. With percent differences of 9.

1% and 0%, along with R2 values of .9996 and .000 (meaning a perfectly horizontal line), the date proved to be nearly exact in compared to the theoretical values. Reason for the little percent difference in the Im vs. Vcm can be attributed to human error in judging exactly where the vertices of the graphs were.

ConclusionAlternating current circuits are found everywhere in the world. From the electricity delivered to millions of businesses and residences in our nation alone to audio and radio signals carried on electrical wire, AC currents and circuits are found everywhere. Civil engineers might relate this knowledge of circuits while designing power lines or transistors for a city or airport. Electrical engineers may apply this knowledge when designing a wiring layout of a radio transmitter or speaker system. While the simplicity of this experiment is basic to AC circuits, knowledge of it is significant to a number of engineering fields.Questions1)    Ohms2)    (1000 Hz)(.5E-3 H) = 3.14 Ohms3)    447214 radians/sec

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