Measurements and Error

ErrorError is the difference between the actual value of a quantity and the value obtained in measurement.There are 2 main types of error

1. Systematic Error

2. Random Error

Systematic Error

Systematic errors are errors which tend to shift all measurements in a systematic way so their mean value is displaced. Systematic errors can be compensated if the errors are known.

Examples of systematic errors are

• zero error, which cause by an incorrect position of the zero point,

• an incorrect calibration of the measuring instrument.

• consistently improper use of equipment.

Systematic error can be reduced by

• Conducting the experiment with care.

• Repeating the experiment by using different instruments.

Zero error1. A zero error arises when the measuring instrument does not start from exactly zero.2. Zero errors are consistently present in every reading of a measurement.3. The zero error can be positive or negative.

(NO ZERO ERROR: The pointer of the ammeter place on zero when no current flow through it.)

(NEGATIVE ZERO ERROR: The pointer of the ammeter does not place on zero but a negative value when no current flow through it.)

(POSITIVE ZERO ERROR: The pointer of the ammeter does not place

on zero but a negative value when no current flow through it.

Random errors

1. Random errors arise from unknown and unpredictable variations in condition.

2. It fluctuates from one measurement to the next.

3. Random errors are caused by factors that are beyond the control of the observers.

4. Random error can cause by

• personal errors such as human limitations of sight and touch.

• lack of sensitivity of the instrument: the instrument fail to respond to the small change.

• natural errors such as changes in temperature or wind, while the experiment is in progress.

• wrong technique of measurement.

• One example of random error is the parallax error.

• Random error can be reduced by

1. taking repeat readings

2. find the average value of the reading.

Parallax errorA parallax error is an error in reading an instrument due to the eye of the observer and pointer are not in a line perpendicular to the plane of the scale.

Ruler, Thermometer, Stopwatch, Ammeter and Voltmeter

• Ruler

1. A metre rule has sensitivity or accuracy accuracy of 1mm.

2. Precaution to be taken when using ruler• Make sure that the object is in contact with the ruler.• Avoid parallax error.• Avoid zero error and end error

Thermometer There are 2 types of mercury thermometer

• Thermometers of range -10oC - 110oC with accuracy 1oC.

• Thermometers of range 0oC - 360oC with accuracy 2oC.

Precaution to be taken when using thermometer

• Make sure that the temperature measured does not exceed the measuring range.

• When measuring temperature of liquid

• immerse the bulb fully in the liquid

• stir the liquid so that the temperature in the liquid is uniform

• do not stir the liquid vigorously to avoid breaking the thermometer

• Stopwatch There are 2 types of stopwatches

1. analogue stopwatches of sensitivity 0.1s or 0.2s

2. digital stopwatches of sensitivity 0.01s.

Ammeter and Voltmeter

1. Ammeters are measuring instrument used to measure electric2. current.

3. An Ammeter is always connected in series with the load (resistor) in a circuit.

4. Voltmeters are measuring instrument used to measure potential difference

5. (voltage).

6. A voltmeter is always connected parallel to the load (resistor) in a circuit.

Consistency, Accuracy and Sensitivity

Consistency1. Precision is the ability of an instrument in

measuring a quantity in a consistent manner with only a small relative deviation between readings.

2. The precision of a reading can be indicated by its relative deviation.

3. The relative deviation is the percentage of mean deviation for a set of measurements and it is defined by the following formula:

Accuracy1. The accuracy of a measurement is the

approximation of the measurement to the actual value for a certain quantity of Physics.

2. The measurement is more accurate if its number of significant figures increases.

4. The accuracy of a measurement can be increased by

• taking a number of repeat readings to calculate the mean value of the reading.

• avoiding the end errors or zero errors.• taking into account the zero and parallax errors.• using more sensitive equipment such as a

vernier caliper to replace a ruler.

5. The difference between precision and accuracy can be shown by the spread of shooting of a tar-get (as shown in Diagram below).

Sensitivity1. The sensitivity of an instrument is its ability to detect small

changes in the quantity that is being measured.2. Thus, a sensitive instrument can quickly detect a small

change in measurement.3. Measuring instruments that have smaller scale parts are

more sensitive.4. Sensitive instruments need not necessarily be accurate. 5. Table above shows that the micrometer screw gauge is

more accurate than the other measuring instruments