Measurements and Instrumentation
This domain covers analog instruments, bridge circuits, error analysis and propagation, transducers, oscilloscopes and digital meters.
Core rules
- A PMMC movement responds to the average value and reads DC only; a moving-iron meter reads RMS and works on both AC and DC; a rectifier meter is calibrated in RMS for sine waves and misreads other waveforms (sine form factor 1.11).
- Range extension: ammeter shunt Rsh = Rm/(m − 1) with m = I/Ifsd; voltmeter multiplier Rse = Rm(m − 1) for m = V/Vfsd.
- Bridge balance: Wheatstone R1/R2 = R3/Rx; Maxwell bridge for inductance, Schering for capacitance and dissipation factor, Wien for frequency.
- Error propagation: for a product or quotient, relative errors add; for sums and differences, absolute errors add.
Worked example
A 1 mA, 50 Ω PMMC movement must read 10 mA full scale. Here m = 10/1 = 10, so Rsh = 50/(10 − 1) = 5.56 Ω. The shunt carries 9 mA while the movement carries 1 mA, and the parallel combination presents about 5 Ω to the circuit. To convert the same movement into a 10 V voltmeter, Rse = 10 V/1 mA − 50 Ω = 9.95 kΩ.
Traps
Using the total meter resistance where the movement resistance belongs; ignoring the shunt's loading effect; expecting true RMS from a rectifier meter on square or triangular waves; and adding relative errors for quantities that should be multiplied rather than summed.