Keywords: physical experiment system error measurement principle correction method detection method
In physics experiment class, it is the most basic experiment in electricity to measure unknown resistance by voltammetry. The purpose of the experiment is to master the basic method of measuring resistance by voltammetry and its error method.
The preliminary understanding of systematic error and accidental error in experiments has been put forward in experimental textbooks and improved in some experiments, and some modifications are needed in some experiments. System errors mainly come from two aspects: first, there are some tendency deviations in the measuring instrument itself, such as the inaccurate quality of the weight itself; Unequal balance arm; Ammeter or voltmeter are not allowed; The thermometer indicates that the value is too large or too small, and so on. On the other hand, it is due to the approximation of the measurement principle or the inconsistency between the measurement method and the theoretical requirements. For example, ignoring some secondary factors in the experimental principle will also make the calculation results deviate from the reality. For example, in Newton's second law experiment, the weight of tractor is calculated only by weight, not by mass; The buoyancy of air is not considered when measuring gravity; The heat exchange with the environment is not considered when measuring heat; When measuring the current or voltage in the circuit, the step-down effect of ammeter and shunt of voltmeter are not considered. Sometimes the observer's operation will also introduce tendentious errors, such as someone's reading is always habitually high or low; When using a stopwatch, some people are always habitually ahead or behind, and so on.
Practice and theory have proved that the probability of accidental error being too large and too small in many measurements is equal, so the average value of many measurements is close to the true value. Both the average method and the line drawing method are used to correct accidental errors. The systematic error is too large or too small for a certain principle, an instrument and an observer, but it has nothing to do with the number of measurements and cannot be corrected by the average method. Therefore, the influence of any kind of system error can be reduced by trying to correct it, but it is difficult to completely find and reduce the actual system error. In practical work, it is necessary to elaborate the principles, methods, measurement steps, used instruments and other factors that may cause system errors, improve the experimental devices and methods through standard instruments, or theoretically correct the measurement results to minimize system errors.
(1) When measuring the resistance value of unknown resistor by internal connection of ammeter, the system error caused by ammeter and its correction method;
1, the circuit shown in the figure, in the ammeter connection mode, because the voltage value u of the voltmeter contains the voltage at both ends of the ammeter. Therefore, the measured value is greater than the actual value of the resistance to be measured. If the internal resistance of ammeter is RA and the resistance to be measured is RX, then:
R=U/I=RA+RX or: rx = r-ra. .....................
2. According to the error theory, measure the phase.
The error is:
△=(R﹣RX)/RX × %
=(RA+RX﹣RX)/RX ×%
= RA/RX×%……②
∴RX=RA/△………………③
① and ② two formulas show that there will be a positive error when measuring unknown resistance with ammeter internal connection method, that is, the measured value R is greater than the true value RX.
① Usage of the formula: If R is measured by the above experiment, RX can be obtained by subtracting RA, and it is easy to correct the system error. Therefore, the internal resistance of ammeter should be marked on the dial, or written on the tape after measurement and attached to the meter.
② Usage of formula: When the systematic error of measurement needs to be estimated, it can be calculated according to this formula before actual measurement. According to this formula, when Ra < < Rx, △→0, the error can be ignored. Therefore, the ammeter internal wiring method is suitable for measuring the resistance with large resistance.
Usage of Formula ③: When we limit the system error △ not to exceed, we can use Formula ③ to calculate the resistance range suitable for this method.
What deserves our attention is that in practical work, we usually have to consider all aspects comprehensively. For example, measure the resistance value, and hope that the smaller the RA, the better. However, the sensitivity of ammeter is relatively small. In order to reduce the accidental error, it is best to rotate the pointer to more than 2/3 of the full scale, but it is likely that the current actually passed has exceeded the allowable current value of the measured resistance. So generally speaking, when the power of high resistance and low resistance is the same, the anti-overload ability is worse, and it is easy to burn out due to overload when measuring large current, so we should pay attention to this in actual measurement.
(2) The system error caused by ammeter and its correction method when measuring unknown resistance with external ammeter.
1, as shown in the circuit, in the external connection of ammeter, the current measured by ammeter includes the current flowing through voltmeter. Therefore, the measured value is less than the actual value of the measured resistance, the internal resistance of the voltmeter is R, and the current passing through it is I, then:
RX=U/(I﹣I)=U/(I﹣U/R)………………④
2. According to the error theory, the relative error is:
△= ×%= ×%
=- ×%= ×%……⑤
∴RX= = ………………⑥
④ and ⑤ two formulas show that there will be negative error when measuring unknown resistance with ammeter internal wiring method, that is, the measured value R is less than the true value RX.
④ Formula usage: If R is measured by the above experiment, RX can be obtained by substituting R, which can conveniently correct the system error. Therefore, the internal resistance of the voltmeter should be marked on the dial, or written on the tape after measurement and attached to the meter.
⑤ Usage of formula: When it is necessary to estimate the systematic error of measurement, it can be calculated according to this formula before actual measurement. According to this formula, when Rx < < R, △→0, the error can be ignored. Therefore, the ammeter internal wiring method is suitable for measuring the resistance with small resistance.
Usage of Formula 6: When we limit the system error △ not to exceed, Formula 6 can be used to calculate the resistance range suitable for this method.
However, in the actual measurement process, it is not always possible to know the approximate resistance of the resistor to be measured in advance, and it is not always clear about the size of RA and R. In order to determine a better connection quickly and accurately, this method is detection.
The steps are as follows:
(1) As shown in the figure, connect the measured resistance R with the ammeter and voltmeter, and the A line K of the voltmeter is empty;
(2) Touch K to the two wires A and B of the ammeter in turn;
③ Compare the reading changes of two ammeters during two contacts: If the voltmeter reading changes obviously, it means that the ammeter has obvious voltage-dividing effect, so the external connection mode should be adopted, and K is connected to A; If the current indicator changes obviously, it means that the shunt function of the voltmeter is obvious, and the internal connection mode should be adopted, and K is connected to B.
In a word, when measuring unknown resistance by "Voltammetry", we should choose the appropriate circuit connection according to the parameters of the electric meter and the size of the measured resistance, so as to reduce or correct the system error, so as to truly achieve the experimental purpose.
[References]
1, University Physics Experiment, Wuhan University of Technology Press
This physical experiment reference book is published by educational institutions.
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