What is the smallest change in the input signal that can be detected by an instrument called?
Resolution
Understanding Instrument Characteristics: Resolution, Accuracy, Precision, and Sensitivity
When we use an instrument to measure something, several characteristics define how well it performs. The question asks about the smallest change in the input signal that the instrument can actually detect and show as a change in its output. Let's look at the options provided and understand what each term means in the context of measurement instruments.
Exploring the Options
Let's define each of the given terms:
- Accuracy: Accuracy refers to how close a measurement is to the true or actual value of the quantity being measured. A highly accurate instrument provides readings that are very near the real value.
- Precision: Precision refers to the reproducibility or consistency of measurements. If you measure the same quantity multiple times with a precise instrument, you will get readings that are very close to each other, even if they are not close to the true value (which would relate to accuracy).
- Resolution: Resolution is the smallest increment of the input signal that the instrument can distinguish and produce a corresponding change in the output reading. It is the minimum step size of the measurement that the instrument can resolve.
- Sensitivity: Sensitivity is the ratio of the change in the instrument's output to a corresponding change in the input signal. It indicates how much the output changes for a given change in the input. A more sensitive instrument will show a larger output change for a small input change.
Identifying the Smallest Detectable Change
The question specifically asks for the term that describes the "smallest change in the input signal that can be detected by an instrument". Based on our definitions above:
- Accuracy deals with closeness to the true value.
- Precision deals with repeatability of measurements.
- Sensitivity relates the magnitude of output change to input change.
- Resolution defines the minimum detectable step in the input signal.
Therefore, the term that precisely matches the description of the smallest detectable change in the input signal is Resolution.
For example, if a digital thermometer can only show temperatures in whole degrees (e.g., 25°C, 26°C), its resolution is 1°C. It cannot detect or display a change smaller than 1°C, even if the actual temperature changes by 0.5°C.
Comparing Instrument Characteristics
It's important to distinguish between these terms. An instrument can be precise but not accurate, or sensitive with poor resolution, and so on.
| Characteristic | What it measures | Analogy |
|---|---|---|
| Accuracy | Closeness to true value | Hitting the bullseye |
| Precision | Reproducibility of measurements | Hitting the same spot repeatedly (even if not the bullseye) |
| Resolution | Smallest detectable input change | The smallest marks on a ruler |
| Sensitivity | Output change per input change | How much the needle moves on a dial for a given change |
Based on the definitions and the comparison, the characteristic that defines the smallest change in the input signal an instrument can detect is Resolution.
Revision Table: Key Instrument Properties
| Term | Definition |
|---|---|
| Resolution | Smallest detectable change in the input signal. |
| Accuracy | Closeness of measurement to the true value. |
| Precision | Reproducibility or consistency of measurements. |
| Sensitivity | Ratio of output change to input change. |
Additional Information on Instrument Characteristics
Understanding instrument characteristics like resolution, accuracy, precision, and sensitivity is crucial in selecting and using instruments correctly. Other important characteristics include:
- Range: The total span of values that the instrument is capable of measuring.
- Linearity: How well the output of the instrument follows a straight line relationship with the input over its range.
- Hysteresis: The difference in output reading for the same input value, depending on whether the input is increasing or decreasing.
- Drift: A change in the instrument's output over time when the input signal is held constant.
While resolution is about the smallest detectable change, sensitivity indicates how responsive the instrument is to changes, and accuracy and precision describe the quality and reliability of the measurement results themselves.
Important Questions from Error Analysis
- Errors that occur after taking care of all gross and systematic errors are called as:
An ammeter of 0-50 A range has an accuracy of ± 1% of full scale reading. The current measured is 10 A. The uncertainty in measured value is
A 0-200 V voltmeter has an accuracy of 0.75% of full-scale reading. If the voltage measured is 100 V, the error is
Suppose that resistors R1 and R2 are connected in parallel to give an equivalent resistor R. If resistors R1 and R2 have tolerance of 1% each the equivalent resistor R for resistor R1 = 300 Ω and R2 = 200 Ω will have tolerance of
A \(4 \frac 1 2\) digit DMM has the error specification as 0.2% of reading +10 counts. If a d.c. voltage of 100 V is read on its 200 V full-scale, the maximum error that can be expected in the reading is
