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HW2 - Fill in the blank columns in the table and on a...

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Homework #2 Physics 132 Consider an experiment where a fixed unknown potential V is to be experimentally determined by connecting various resistances R and measuring the current I. Suppose that it is known that this potential source, shown as a “black box” in the sketch above, has a very low internal impedance and can be thought of as an ideal voltage source. The idea is to use Ohm’s law, V=I*R, to determine the unknown potential V. In principle you would only need to use one measurement to determine V, but the strategy is to “over determine” the measurement so as to experimentally explore the systematic and random errors involved. The resistors used are +/-1%, and the reading error of the ammeter is +/- 0.1 mA. For each of 4 values of resistance ( 1, 2, 4, and 8 k Ω ) the measured current in mA is recorded in the table below. R (k Ω ) 1% I +/- 0.1 (mA) Relative error on I (%) I*R Relative error on VI (%) 1.00 6.7 2.00 4.1 4.00 2.2 8.00 1.1 1)
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Unformatted text preview: Fill in the blank columns in the table and on a separate sheet, determine V along with an error estimate using first a simple average and then a weighted average. For each case state the mean value, the standard deviation of the data, and the standard deviation of the mean. Show all your work (use no more automation than a hand calculator). 2) State at least two clear evidences from the data that there is some form of systematic error in the experiment. 3) It turns out that there is a 500 Ω resistance to the ammeter that was left out of the sketch. Assuming that you had guessed correctly that such a resistance might be the problem, how could you have determined this resistance value from the data (state the procedure)? 4) In view of the new theory, and assuming a 500 Ω resistance, now determine V along with an error estimate. 5) Keeping the assumption that V is a constant, compare the estimated and observed random errors in this experiment....
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