lab5RCCircuit

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Dec 6, 2023

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Nazar Kabylov, David Morgan PHYSICS 212 February 17, 2022 Lab 5 Data and Observations Theory: In this lab we are analyzing capacitors and resistors in an RC circuit.From a power supply that is sending charge to a capacitor, the capacitor will gain charge to a maximum amount and will have an equivalent voltage. once charge is stopped being sent the capacitor in an RC circuit will equalize to neutral charge over time equal to the function V = V 0 ∗ e − t / RC Since voltage is proportional to charge related by Q=CV the same function applies replacing V and V0 with Q and Q0. Q is the charge, V is the voltage, t is time, R is the resistance of the resistor, and C is the capacitance of the capacitor. This function is an exponential where graphing the voltage vs time leads to a decreasing exponential graph shown in the V vs t graphs. For analysis sake a linear graph is easier so taking the natural log of both sides of our functions gives us ln ( V )= ln ( V 0 )− t / RC . When we graph LN(V) vs time we get a linear graph and the slope is equal to -1/RC. if we know the capacitance and the slope we can calculate the value of the resistance. Setup: The setup included a 5.6 microFarad capacitor, a simple switch, two multimeters (used as voltmeters) as well as a power supply and wires to connect everything. We set up a parallel circuit with the switch being in series, and the capacitor and the multimeter in parallel. We have also used a phone stopwatch for our time intervals.

Procedure: To gather data to analyze the resistance of our multimeters we started with setting our power supply to 5 volts using the capstone software. After closing the switch this starts to charge the capacitor until it reaches the voltage of the power supply. We then open a switch and start a stopwatch with the time at zero. The multimeter will show progressively decreasing reading, meaning that the voltage is decreasing. The readings are recorded at certain time intervals which depend on the multimeter used. With the fluke multimeter which has a higher internal resistance we used intervals of 10 seconds to take voltages readings. With the cen-tech multimeter we recorded every 1 second. Both multimeter readings were recorded until the voltage decreased to less than 10% of the initial voltage. The value of least precision was of the multimeter was recorded too and it was 0.001V .

Summary: As the function starts as an exponential we can’t use simple software to create a trendline with a regression value so we use the natural log to linearize it first. When we take the natural log of both sides of the equation we get a function we can plot which will be linear as we see by our plots and this allows us to get regression values. Very surprising we see a value of 1 on

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the graph using the fluke multimeter, I have never seen that but I guess we got great data. With the centech multimeter we got a value of .9997 which is quite accurate. on both graphs our standard deviations were very small so its difficult to see the error bars and by the fact we got a 1 regression leads me to believe as well that our error was small. the magnitude of the standard deviation was in the .001’s and the voltages were in the 1’s. after getting slope values from the graphs we calculated our resistance ratings for the two multimeters, for the fluke one we had a slope of -.0146 and the capacitance was 5.6*10^-6 farads. we got a resistance of 12.23 mega ohms. with the centech multimeter we had a slope of -.1623 and the same capacitance. thus a resistance of 1.1 mega ohms. we see a very large difference in the two resistances and we read that the value of resistance of each multimeter is a decent judge of the quality of the product.

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