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4 Pages

### Physics lab11

Course: ENG 101, Spring 2010
School: Montgomery College
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Word Count: 749

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purpose Introduction The of this lab is to manipulate AC, RC and RL circuits and to analyze all the parameters such as the period, phase angles, and the graphs. Procedure Hardware: - Analog Oscilloscope - AC Function generator - Resistors (10k) - Capacitor(0.1uF) - Inductor (25mH) Experiment: In the first part of the experiment, we set up an RC circuit to a function generator. We then connected two channels of...

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purpose Introduction The of this lab is to manipulate AC, RC and RL circuits and to analyze all the parameters such as the period, phase angles, and the graphs. Procedure Hardware: - Analog Oscilloscope - AC Function generator - Resistors (10k) - Capacitor(0.1uF) - Inductor (25mH) Experiment: In the first part of the experiment, we set up an RC circuit to a function generator. We then connected two channels of the oscilloscope to the circuit by hooking the first channel to display the voltage signal and the second channel to display the signal across the capacitor. We then triggered the oscilloscope and set up the function generator on a frequency high enough to display the waves forms in such a way that Vr = Vin. We then use the dual trace feature of the oscilloscope to make phase measurements over a sufficiently wide range of frequencies to plot the graph of tan vs. 1/ In the second part of the experiment, we set up an RL circuit by connecting a 25mH inductor in series with a 1k resistor. We then set it and collect a set of data of , to get tan () and In the last part of the experiment, we set up again an RL circuit and record V L and Vr. We then find a frequency high enough so that VL and VR have the same amplitude and verify that the phase angle comes out approximately to 90 Data/Results/Analysis 1- Our measured resistance and capacitance are R = 10.33k and C = 10-4F In order for us to figure out the phase, we measure t and T. t = 0.7div * 0.1ms/div = 0.7*10-4s T = 5.7 div * 0.1ms/div = 5.7*10-4s To calculate the phase angle, we could use: Cos () = Vr/E Cos () = 3.33/4.42 = 0.77 rad Or = 2 = 2 x0.7/5.7 = 0.72 rad 2- 3- Using the first formula, our calculation are summarized below: Vr Vs(V) Vc (V) (V) (rad) 1.843 4.42 2.7 3.33 0.72 2.545 4.46 2.08 3.73 0.58 3.524 4.62 1.56 4.14 0.46 4.868 4.67 1.01 4.35 0.37 6.527 4.64 0.79 4.41 0.32 10.15 5.14 0.02 4.96 0.27 Using the second formula, we get: t (s) T (s) (rad) 0.7 x 10-3 5.7 x 10-3 0.77 0.4 x 10-4 4 x 10-4 0.63 20 x 10-6 285 x 10-6 0.44 12 x 10-6 210 x 10-6 0.36 8 x 10-6 154 x 10-6 0.33 4.0 x 10-6 100 x 10-6 0.25 To find tan(), we use the values of in the first table since they were obtained using the DMM whereas those in the second table were obtained using the Oscope; the latter are therefore likely to be less accurate. Our table of tan() follows: Tan ( ) 0.87706 8 0.655168 0.495449 0.38786 3 0.331389 0.276758 1/ 0.542 594 0.392 927 0.283 768 0.205 423 0.153 21 0.098 522 The follows: To graph derive RC, we use: Tan () = 1/ * (1/RC) = tan() Therefore, 1/RC is the slope of the graph. Thus, RC = 1/ 0.7267 RC = 1.37s The measure value of RC is RC = 10.33 x x 0.1 x RC = 1.033 s The percent difference between those two values is P = 23% 4- Lets calculate - - for all the values E(V) (V) (V) -- 4.42 2.7 3.49 0.06 4.46 2.08 3.93 0.12 4.62 1.56 4.34 0.07 4.67 1.01 4.55 0.08 4.64 0.79 4.51 0.56 5.14 0.02 5.06 0.81 5- Using tan () = , we get the following table: 0.93 1.4 1.56 2.41 2.78 3.17 3.81 4.53 4.14 4.06 4.03 3.72 3.54 3.29 3.01 2.5 tan () 0.224638 0.344828 0.387097 0.647849 0.785311 0.963526 1.265781 1.812 1.556 1.990 2.226 3.736 4.539 5.586 7.519 10.56 The graph follows: From our graph, we can conclude that 0.2739 is our value of L/R Theoretically, L/R = 24.79*10-3 / 1000 = 2.479*10-5. The percent difference between the tow values is P = 10.48% 6- The amplitude of the twp signals is = 5.83KHz. And our reading of t = 2.2div * 20us/div = 44us and T = 3.5div * 50us/div = 175 us. From those two values, we can derive = 360 * t/ T = 360 * 44*10-6/ 175 * 10-6 = 90.5 So = 90.5 Compared to the 90, we get a 0.55% error which is negligible Explanation/Interpretation Our value for - - is close to zero which verifies Pythagorean Theorem. Our overall percentages are a little high and this could be due to mishandling in the experiment and inaccuracies which might have occurred during the readings measurements. In the last calculation, 90.5 are very close to 90 degree. Therefore, we are in an acceptable range of error. Post-lab questions 1- R = V/I, C = Q/V RC = Q/I I = Q/t RC = Q/(Q/t) = t Therefore, RC is a unit of time. 2. R = V/I, C = Q/V, L = v(t) dt/di L = Henry = (volt*sec/amp)(rad/sec) = V/A = 1/ C = 1/((rad/sec)(Coulomb/volt)) =(sec)(volt)/(coulomb) A= Coulomb/sec = V/A 1/ C = V/A = 3. F(x) = cos(t + ) F(x) = -sin(t + ) F(x) = -2cos(t + ) F(x) = 3sin(t + ) 4. If the internal resistance of the inductor is negligible it will shorten the relative phase of the voltage across the inductor and heighten the current through it. This effect will be of greater importance at lower frequencies Conclusion The lab was well conducted with minor mistakes. The purpose was reached, although we made a few errors, but the overall principle of the AC, RC and RL circuits was understood.
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