📚 Zero Error | 零误差
In physics experiments, accurate measurement is crucial. A measurement error that often goes unnoticed is zero error, which occurs when a measuring instrument displays a non-zero reading even when the quantity being measured is zero. This systematic error can affect the accuracy of results if not corrected.
在物理实验中，准确测量至关重要。一种常被忽视的测量误差是零误差，当测量仪器在被测量为零时显示非零读数，就会出现这种情况。如果不加以校正，这种系统误差会影响结果的准确性。
1. Understanding Zero Error | 理解零误差
Zero error is a type of systematic error inherent in a measuring instrument. It is caused by factors such as manufacturing imperfections, wear and tear, or improper calibration. For example, a micrometer screw gauge may show 0.01 mm when the anvil and spindle are fully closed. This means every reading taken with that instrument will be larger by 0.01 mm than the true value.
零误差是测量仪器固有的一种系统误差。它由制造缺陷、磨损或校准不当等因素造成。例如，螺旋测微器的砧座和心轴完全闭合时可能显示0.01毫米。这意味着使用该仪器进行的所有读数都将比真实值大0.01毫米。
Zero error is not a random error; it is consistent and repeatable. Once identified, it can be mathematically removed from all measurements taken with the same instrument.
零误差不是随机误差；它具有一致性和可重复性。一旦识别出来，就可以通过数学方法从该仪器所有测量结果中消除。
2. Types of Measuring Instruments | 测量仪器类型
Instruments commonly affected by zero error include vernier calipers, micrometer screw gauges, ammeters, and voltmeters. Each has its own way of indicating zero error.
常见受零误差影响的仪器包括游标卡尺、螺旋测微器、电流表和电压表。每种仪器都有自己的零误差指示方式。
Vernier calipers display zero error when the jaws are closed.
游标卡尺在钳口闭合时显示零误差。
Micrometer screw gauges show zero error when the anvil and spindle meet.
螺旋测微器在砧座与心轴接触时显示零误差。
Ammeters and voltmeters may have a non-zero pointer position with no current or voltage.
电流表和电压表在没有电流或电压时指针可能不在零位。
3. Types of Zero Error: Positive and Negative | 零误差类型：正误差与负误差
Zero error can be either positive or negative. For a micrometer screw gauge, if the zero mark on the thimble is below the datum line on the sleeve, the error is positive. If it is above the datum line, the error is negative.
零误差可以是正误差或负误差。对于螺旋测微器，如果棘轮上的零刻度低于套筒上的基准线，则为正误差；如果高于基准线，则为负误差。
For a vernier caliper, with the jaws closed, if the zero of the vernier scale lies to the right of the main scale zero, the error is positive; if it lies to the left, the error is negative.
对于游标卡尺，在钳口闭合时，如果游标尺的零刻度位于主尺零刻度的右侧，则为正误差；如果位于左侧，则为负误差。
For ammeters and voltmeters, a pointer resting above zero when no current flows is a positive error; resting below zero is a negative error.
对于电流表和电压表，无电流时指针停在零刻度以上为正误差；停在零刻度以下为负误差。
4. How to Identify Zero Error | 如何识别零误差
To identify zero error, close the instrument fully and observe the reading. For a vernier caliper, bring the jaws together; for a micrometer, turn the ratchet until the anvil and spindle just touch. For electrical instruments, disconnect the circuit and check the pointer.
要识别零误差，应将仪器完全闭合并观察读数。对于游标卡尺，让钳口闭合；对于螺旋测微器，转动棘轮直至砧座与心轴刚好接触。对于电气仪器，断开电路并检查指针。
It is important to record the zero error before beginning the experiment and to note its sign. In an exam, you may be given a diagram showing the zero position, so you must be able to interpret it correctly.
在开始实验前记录零误差并注明其正负号非常重要。考试中可能会提供显示零位置的示意图，因此你必须能够正确解读。
5. Correcting Zero Error | 校正零误差
The correction is straightforward: for a positive zero error, subtract the zero error from the measured reading; for a negative zero error, add the absolute value of the zero error.
校正很简单：对于正零误差，从测量读数中减去零误差；对于负零误差，加上零误差的绝对值。
Actual Reading = Measured Reading − Zero Error
Here, zero error is positive if the instrument reads too high, and negative if it reads too low. The sign of the zero error must be included when substituting into the equation.
这里，零误差为正表示仪器读数偏高，零误差为负表示读数偏低。代入公式时，零误差必须带上正负号。
6. Example with Vernier Caliper | 游标卡尺示例
This is a positive zero error of +0.02 cm. The corrected length is 3.42 − 0.02 = 3.40 cm.
假设游标卡尺测得某物体为3.42厘米。闭合钳口时，发现游标尺的零刻度在主尺零刻度的右侧0.02厘米处。这是+0.02厘米的正零误差。校正后的长度为3.42 − 0.02 = 3.40厘米。
zero error would be −0.02 cm, and the corrected reading would be 3.42 − (−0.02) = 3.44 cm.
如果游标尺的零刻度位于左侧0.02厘米处，则零误差为−0.02厘米，校正后的读数为3.42 − (−0.02) = 3.44厘米。
7. Example with Micrometer Screw Gauge | 螺旋测微器示例
.01 mm, so the zero error is −0.03 mm. The corrected diameter is 1.55 − (−0.03) = 1.58 mm.
螺旋测微器测得线径为1.55毫米。当砧座和心轴闭合时，棘轮上的零刻度在基准线上方3个刻度处。每刻度为0.01毫米，因此零误差为−0.03毫米。校正后的直径为1.55 − (−0.03) = 1.58毫米。
e zero error would be +0.02 mm. The corrected reading would then be 1.55 − 0.02 = 1.53 mm.
如果零刻度在基准线下方2个刻度处，则零误差为+0.02毫米。校正后的读数则为1.55 − 0.02 = 1.53毫米。
8. Zero Error in Electrical Instruments | 电气仪器中的零误差
Ammeters and voltmeters often have a small zero error. With no current or voltage, the pointer may not rest exactly at zero. This can be corrected by using the zero-adjust screw on the instrument, or by recording the offset and subtracting it from every reading.
电流表和电压表常有微小的零误差。在没有电流或电压时，指针可能不完全停在零位。可以通过仪器上的调零螺丝进行校正，或者记录偏移量并从每次读数中减去。
In digital instruments, zero error may appear as a non-zero reading on the display when no input is applied. Some digital meters allow zero calibration, but if not, the offset must be subtracted mentally.
在数字仪器中，零误差可能表现为无输入时显示器上的非零读数。一些数字仪表允许零点校准，但若不具备该功能，则必须在心中减去该偏移量。
9. Zero Error vs. Other Errors | 零误差与其他误差
Zero error is a systematic error and affects all measurements in the same way. Random errors are unpredictable and can be reduced by averaging multiple readings. Other systematic errors include parallax error, where the reading changes with the observer's line of sight, and calibration errors.
零误差是一种系统误差，对所有测量的影响一致。随机误差不可预测，可通过多次测量取平均来减小。其他系统误差包括视差误差（读数随观察者视线方向而变化）以及校准误差。
Unlike zero error, random errors cannot be completely eliminated; they can only be minimized by careful technique and repeated measurement. Zero error, however, can be removed exactly by applying the correction.
与零误差不同，随机误差无法完全消除，只能通过仔细操作和重复测量来最小化。而零误差则可以通过校正精确地去除。
10. Importance in A-Level Exams | 在A-Level考试中的重要性
In AQA A-Level Physics, you may be required to record zero error and apply the correction. It is essential to state whether the zero error is positive or negative and to subtract the zero error from every measured reading. A common mistake is forgetting to apply the correction, leading to a systematic error in the final result.
在AQA A-Level物理考试中，可能要求记录零误差并加以校正。必须明确零误差的正负性，并从每个测量读数中减去零误差。常见错误是忘记校正，导致最终结果产生系统误差。
Questions often describe a zero error and ask you to find the true value. You must pay close attention to the wording: "zero error is +0.02 mm" means you subtract 0.02 mm; "zero error is −0.02 mm" means you add 0.02 mm.
考题常描述一种零误差并要求求真实值。你必须仔细注意措辞：“零误差为+0.02毫米”意味着减去0.02毫米；“零误差为−0.02毫米”意味着加上0.02毫米。
11. Worked Exam-style Question | 考试风格例题
A student uses a micrometer screw gauge to measure the diameter of a wire. The measured reading is 2.35 mm. The zero error is determined to be +0.04 mm. Calculate the actual diameter of the wire.
一名学生使用螺旋测微器测量一根导线的直径。测量读数为2.35毫米。已知零误差为+0.04毫米。计算该导线的实际直径。
Actual diameter = Measured reading − Zero error = 2.35 mm − 0.04 mm = 2.31 mm
The correction is negative because the instrument reads too high by 0.04 mm, so the actual diameter is 2.31 mm.
校正为负数，因为仪器读数偏高0.04毫米，因此实际直径为2.31毫米。
12. Summary and Common Pitfalls | 总结和常见误区
Always check for zero error before starting measurements. Remember the correction rule: actual reading equals measured reading minus zero error. Be careful with the sign convention for different instruments. Also, avoid confusing zero error with zero correction; they are the same concept, but the sign matters.
开始测量前务必检查零误差。记住校正规则：实际读数等于测量读数减去零误差。注意不同仪器的符号约定。此外，避免混淆零误差与零点修正；它们是同一个概念，但符号至关重要。
Common pitfalls include:
常见误区包括：
Reading the zero error scale in the wrong direction.
读零误差刻度时方向错误。
Forgetting the sign when subtracting a negative zero error.
减去负零误差时忘记符号。
Not checking the zero reading before measuring.
测量前未检查零读数。
Applying the correction incorrectly for digital instruments.
对数字仪器错误地应用校正。
Published by TutorHao | Physics Revision Series | aleveler.com
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