Capacitators Lab

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California Polytechnic State University, Pomona *

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Electrical Engineering

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Apr 3, 2024

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Lab 05 – Capacitors Part A: Measurement of Unknown Capacitance The formula you need to use to calculate the unknown capacitance in terms of the known capacitance and the voltages is ࠵శ࠵? unk = ࠵శ࠵? � ࠵౉࠵? ps ࠵౉࠵? − 1 � We take the known capacitor to be the 10 ࠵༇࠵? F capacitor, and for the unknown capacitor, we use the 22 ࠵༇࠵? F and 47 ࠵༇࠵? F capacitors. Record your data and the result of your calculations of the experimental values. Then find the % difference between the experiment and the theory. Unknown Capacitor 1 Unknown Capacitor 2 Power Supply Voltage ( ࠵౽࠵? ࠵఩࠵?࠵఩࠵? ) (V) Voltage Across the Unknown Capacitor ( ࠵౽࠵? ) (V) Experimental Value of Unknown Capacitor ( ࠵౪࠵? ࠵ఞ࠵?࠵ఞ࠵? ) ( ࠵ཁ࠵?࠵ཁ࠵? ) Theoretical Value of Unknown Capacitor ( ࠵౪࠵? ࠵భ࠵?࠵భ࠵? ) ( ࠵ཁ࠵?࠵ཁ࠵? ) %Diff of ࠵౪࠵? ࠵ఞ࠵?࠵ఞ࠵? and ࠵౪࠵? ࠵భ࠵?࠵భ࠵? Given the experimental circumstances, a % Diff of up to 10% is acceptable. If you have a higher than 10%, you may check your work again. For the second unknown capacitor a higher % diff is acceptable. The % Diff for this one should be less than 20%. 5V 5V 1.6 V 0.658 46.75 43.01 8.24% 310.14 266.8 12.4% Ryan Santos

Part B: Series and Parallel Combinations Repeat the experiment as in Part A, but this time use the Series and parallel combinations of the two capacitors as the unknown. Record your results in the table below. The theoretical value of the combination is the equivalent capacitance of 22 and 47 ࠵༇࠵? F in series or parallel. Series Combination Parallel Combination Power Supply Voltage ( ࠵౽࠵? ࠵಑࠵?࠵಑࠵? ) (V) Voltage Across the The combination ( ࠵౽࠵? ) (V) Experimental Value of The Combination ( ࠵౪࠵? ࠵ಆ࠵?࠵ಆ࠵? ) ( ࠵ཁ࠵?࠵ཁ࠵? ) Theoretical Value of The Combination ( ࠵౪࠵? ࠵ಕ࠵?࠵ಕ࠵? ) ( ࠵ཁ࠵?࠵ཁ࠵? ) %Diff of ࠵౪࠵? ࠵ಆ࠵?࠵ಆ࠵? and ࠵౪࠵? ࠵ಕ࠵?࠵ಕ࠵? Part C: Measurement of the Internal Resistance, R , of the Voltmeter For each one of the available capacitors measure the time for the voltage to drop to half of its initial value ( ࠵ಕ࠵? ࠵࿏࠵? / ࠵࿐࠵? ). Initial Voltage is denoted ࠵౽࠵? ࠵࿎࠵? . The formula to use for calculating the internal resistance R is: ࠵౅࠵? = ࠵ౡ࠵? 1 / 2 /( ࠵శ࠵? ࠵ౙ࠵?࠵ౙ࠵? 2 ) . ࠵࿏࠵?࠵࿎࠵? ࠵ཁ࠵?࠵ཁ࠵? Capacitor ࠵࿐࠵?࠵࿐࠵? ࠵ཁ࠵?࠵ཁ࠵? Capacitor ࠵࿒࠵?࠵࿕࠵? ࠵ཁ࠵?࠵ཁ࠵? Capacitor Initial Voltage ( ࠵౽࠵? ࠵࿎࠵? ) (V) ( ࠵౽࠵? ࠵࿎࠵? / ࠵࿐࠵? ) (V) ࠵ಕ࠵? ࠵࿏࠵? / ࠵࿐࠵? (s) ࠵౹࠵? ( ࠵ఌ࠵?࠵ఌ࠵? ) To compare your experimental values of R , find the %Diff of the maximum and the minimum of the three values you calculated for R as %Diff = | ࠵ీ࠵?࠵ీ࠵?࠵ీ࠵? − ࠵ీ࠵?࠵ీ࠵?࠵ౙ࠵? | ࠵౅࠵? � × 100% = 5V 5V 1.8 4.46 4.46 5 2.5 2.23 92 460 4.65 2.325 77 39.11 27.49 29.7% 5.69 3.86 32% 11.1 6.03 14.11 57.26%

Part D: Measurement of the Time Constant Follow the procedure in the lab manual for 22 ࠵༇࠵?࠵༇࠵? capacitor. The formulae to use in this part is the exponential decay of the voltage for the discharge of a capacitor: ࠵౉࠵? = ࠵౉࠵? 0 ࠵౒࠵? −࠵ౡ࠵? / ࠵༏࠵? or ln ࠵౉࠵? = − 1 ࠵༏࠵? ࠵ౡ࠵? + ln ࠵౉࠵? 0 Set the power supply to 4 volts. So, use a stopwatch to measure the time for the voltage to get to the following values from the beginning, and fill in the rest of the table accordingly. You may use the time of the video instead of a stopwatch. Voltage ࠵౽࠵? (V) ࠵ಕ࠵? (min:s) t (s) ࠵థ࠵?࠵థ࠵? ࠵౽࠵? 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 Once the table is complete, in an Excel workbook, make a graph of ln( ࠵౉࠵? ) versus the time ࠵ౡ࠵? , and make the line of best fit to the data. Then extract the slope of the best fit line. Include the graph with the equation of best fit line at the end of this document. What does the slope represent? _____ ࠵ె࠵?࠵ౙ࠵?࠵ె࠵?࠵ె࠵?࠵౒࠵? ࠵౉࠵?࠵ీ࠵?࠵ౙ࠵?࠵౉࠵?࠵౒࠵? = ________ Using the slope value, find the time constant for this circuit. Call this the experimental value ࠵༏࠵? ࠵౒࠵?࠵౒࠵?࠵౒࠵? = ________ Then compare this value with what you expect theoretically, using the average R value from Part C and the Capacitance used ( ࠵శ࠵? = 22 ࠵༇࠵?࠵༇࠵? ). ࠵༏࠵? th = ࠵౅࠵? ave ࠵శ࠵? = 29 12 20 20 22 23 26 33 37 43 51 64 80 115 0:12 0:20 0:20 0:22 0:23 0:26 0:29 0:33 0:37 0:43 0:51 1:04 1:20 1:55 -0.0219 -1/T 45.66 229.02 1.386 1.322 1.253 1.179 1.099 1.012 0.916 0.811 0.693 0.559 0.405 0 -0.288 -0.693

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