Electrical Instrumentation and Measurement Principles
Strain Measurement with Strain Gauges
A strain gauge is a resistive transducer that changes its electrical resistance in proportion to the mechanical strain applied to it.
Principle and Gauge Factor
When a conductor is stretched, its length increases and diameter decreases, both of which increase resistance (R = ρL/A). The Gauge Factor (GF) is defined as: GF = (∆R/R) / (∆L/L) = (∆R/R) / ε, where ε is strain. For metallic gauges, GF ≈ 2; for semiconductor gauges, GF = 100–150.
Wheatstone Bridge Circuit
The strain gauge forms one arm of a Wheatstone bridge. At no strain, V_out = 0. When strain is applied, the output voltage is V_out = (Vs × GF × ε) / 4 for a quarter-bridge configuration. Bridge configurations include quarter, half, and full-bridge setups to increase sensitivity and provide temperature compensation using a dummy gauge.
Cathode Ray Oscilloscope (CRO)
The CRO is a vital tool for visualizing electrical signals. Its major sections include:
- Cathode Ray Tube (CRT): Produces and focuses an electron beam onto a phosphor screen.
- Vertical (Y) Amplifier: Amplifies input signals for vertical deflection.
- Trigger Circuit: Synchronizes the time base with the input signal for a stable display.
- Time Base Generator: Generates a linear sawtooth waveform for horizontal (X) deflection.
- Power Supply: Provides high voltage for the CRT and low voltage for internal circuits.
Digital Voltmeters (DVM)
A Ramp-type DVM converts analog voltage to digital readings by measuring the time interval required for a linear ramp voltage to equal the unknown input voltage. While simple, accuracy depends on ramp linearity and clock stability. Dual-slope DVMs offer higher accuracy by integrating the input over a fixed period.
Flow Measurement Technologies
Electromagnetic Flow Meters
Based on Faraday’s Law, these meters measure the EMF induced in a conducting fluid moving through a magnetic field. They are ideal for slurries and offer no obstruction to flow.
Ultrasonic Flow Meters
These use either the Transit-Time method (measuring time difference between upstream and downstream pulses) or the Doppler method (measuring frequency shift from particles) to determine flow velocity without physical contact.
Temperature Measurement Devices
- RTD (Resistance Temperature Detector): Uses the predictable resistance change of metals (e.g., PT100). Offers high accuracy and linearity.
- Thermistor: A semiconductor device with high sensitivity but non-linear response.
- Thermocouple: Generates an EMF based on the Seebeck effect at the junction of two dissimilar metals.
- Radiation Pyrometer: Enables non-contact measurement of high temperatures via thermal radiation.
Magnetic and Electrical Measurements
Ballistic Galvanometer and Fluxmeters
Used to measure total charge or flux changes. The Fluxmeter is a specialized galvanometer with negligible restoring torque, making it ideal for flux integration.
Lloyd-Fisher Square
A specialized apparatus used to measure iron losses (hysteresis and eddy current) in magnetic sheet materials by creating a closed magnetic circuit.
DC Potentiometer
A null-type instrument that measures voltage by comparing it to a standard cell, ensuring no current is drawn from the source under test, thus eliminating loading errors.
Instrument Characteristics
- Accuracy: Closeness to the true value.
- Resolution: Smallest detectable change.
- Precision: Consistency of repeated measurements.
PMMC and Moving Iron Instruments
- PMMC: Uses a permanent magnet and moving coil; provides a linear scale and is suitable for DC.
- Moving Iron (MI): Operates on the attraction or repulsion of iron pieces; suitable for both AC and DC with a non-linear (squared) scale.
Power Measurement
The Two-Wattmeter Method is the standard for measuring power in 3-phase systems. Total power is the sum of the two readings, and the power factor can be derived using the ratio of their difference to their sum.