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
± 5%
Ammeter Uncertainty Calculation Explained
This solution explains how to calculate the uncertainty in a current measurement using an ammeter, considering its accuracy specifications.
Understanding the Problem
We are given an ammeter with the following details:
- Range: 0-50 A (This means the Full Scale Reading, FSR, is 50 A)
- Accuracy: $\pm 1\%$ of Full Scale Reading (FSR)
- Measured Current: 10 A
The goal is to find the uncertainty in the measured value of 10 A, expressed as a percentage of the measured value itself.
Calculating Absolute Uncertainty
The accuracy specification tells us the maximum error relative to the full scale reading. First, we calculate the absolute uncertainty:
Absolute Uncertainty = Accuracy Percentage $\times$ Full Scale Reading (FSR)
Absolute Uncertainty = $1\% \times 50 \, \text{A}$
Absolute Uncertainty = $\frac{1}{100} \times 50 \, \text{A}$
Absolute Uncertainty = $0.5 \, \text{A}$
This means the ammeter reading can be off by as much as $0.5 \, \text{A}$ from the true value.
Determining Percentage Uncertainty of Measured Value
The question asks for the uncertainty relative to the *measured value* (10 A), not the full scale reading.
Percentage Uncertainty = $ \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100\% $
We substitute the values we have:
Percentage Uncertainty = $ \left( \frac{0.5 \, \text{A}}{10 \, \text{A}} \right) \times 100\% $
Percentage Uncertainty = $ 0.05 \times 100\% $
Percentage Uncertainty = $ 5\% $
Final Uncertainty
Therefore, the uncertainty in the measured value of 10 A is $\pm 5\%$.
Summary Table
| Parameter | Value | Calculation/Notes |
|---|---|---|
| Ammeter Range (FSR) | 50 A | Given |
| Accuracy Specification | $\pm 1\%$ of FSR | Given |
| Absolute Uncertainty | $0.5 \, \text{A}$ | $1\% \times 50 \, \text{A}$ |
| Measured Current | 10 A | Given |
| Uncertainty (% of Measured Value) | $\pm 5\%$ | $(0.5 \, \text{A} / 10 \, \text{A}) \times 100\%$ |
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