Measuring Instruments and Errors
Errors and accuracy, PMMC, moving iron, electrodynamometer and rectifier instruments, extension of ranges with shunts and multipliers, loading effect, and instrument transformers.
Measurements are only as good as the instruments and how they are used. GATE asks which instrument suits AC or DC, how to extend ranges, and how errors combine.
Errors
- Accuracy: closeness to the true value. Precision: closeness of repeated readings to each other. Resolution: smallest detectable change.
- Types: gross (human), systematic (instrumental, environmental, loading) and random errors.
- Limiting (guarantee) error is quoted as a percentage of full-scale, so the relative error grows at lower readings: a ±1% of full-scale instrument reading at half-scale has ±2% error.
- Combining errors: for a sum or difference, absolute errors add; for a product or quotient, relative (percentage) errors add; for a power xⁿ, n times the relative error.
Analog instruments
| Instrument | Works on | Scale | Reads |
|---|---|---|---|
| PMMC | Force on a coil in a permanent magnet field | Linear | DC only (average value) |
| Moving iron (attraction, repulsion) | Iron vane in a coil's field, T ∝ I² | Non-linear (cramped at the start) | AC and DC (RMS) |
| Electrodynamometer | Fixed and moving coils | Non-linear for V and I; linear as a wattmeter | AC and DC, transfer standard |
| Rectifier type | PMMC + diode bridge | Calibrated in RMS for sine waves | AC (errors for non-sinusoidal waves) |
| Thermocouple / hot-wire | Heating effect | Square law | True RMS, high frequency |
Damping: eddy-current damping (PMMC), air-friction damping (moving iron). Controlling torque: springs or gravity.
Extending ranges
- Ammeter shunt: R_sh = R_m I_m/(I − I_m) = R_m/(m − 1), with m = I/I_m.
- Voltmeter multiplier: R_se = V/I_m − R_m = R_m(m − 1).
- Voltmeter sensitivity (Ω/V) = 1/I_fs. A low-sensitivity voltmeter loads a high-resistance circuit and reads low.
Instrument transformers
- CT (current transformer): steps current down (for example 1000/5 A). Its secondary must never be opened while the primary carries current: dangerously high voltage and core saturation.
- PT (potential transformer): steps voltage down (for example 11 kV/110 V).
- Errors: ratio error and phase-angle error.
Worked example
A PMMC meter with 1 mA full-scale and 100 Ω resistance is to read 10 V.
- Multiplier = 10/0.001 − 100 = 9900 Ω. Sensitivity = 1000 Ω/V.
Practice
A 0–100 V voltmeter has a guaranteed accuracy of 2% of full scale. What is the possible percentage error when it reads 50 V?
Show answer and explanation
Answer: 4Error = ±2 V; at 50 V this is ±4%.
A meter with R_m = 50 Ω and full-scale current 1 mA must measure 1 A. What shunt resistance (mΩ) is needed? (Give 2 decimal places.)
Show answer and explanation
Answer: 50.05R_sh = R_m I_m/(I − I_m) = 0.05/0.999 = 0.05005 Ω = 50.05 mΩ.
Power is found as P = V I. V has ±1% error and I has ±2% error. What is the maximum percentage error in P?
Show answer and explanation
Answer: 3For a product, relative errors add: 1% + 2% = 3%.
Which instrument can measure only DC?
Show answer and explanation
Answer: AThe PMMC torque reverses with current direction, so it reads the average, which is zero for AC.