Electrical and Electronic Measurements
What is Electrical and Electronic Measurements?
The closeness of a measured value to the true or accepted value of the quantity being measured.
Key formula / rule: PMMC Deflecting Torque
Key points
- Understand the operating principles, construction, and characteristics of various analog and digital measuring instruments.
- Analyze the sources of errors in measurements and apply methods for their reduction and compensation.
- Select appropriate measuring instruments and techniques for specific electrical parameter measurements.
- Apply bridge methods for precise measurement of resistance, inductance, and capacitance.
Common exam trap
Confusing the application of PMMC (DC only) and MI (AC/DC) instruments.
Definitions
- Term
Accuracy
- Meaning
The closeness of a measured value to the true or accepted value of the quantity being measured.
- Term
Precision
- Meaning
The ° to which repeated measurements under unchanged conditions show the same results; a measure of reproducibility.
- Term
Resolution
- Meaning
The smallest change in the input quantity that causes a detectable change in the instrument's output reading.
- Term
Sensitivity
- Meaning
The ratio of the change in output signal or response to a change in the input quantity being measured.
- Term
Systematic Error
- Meaning
Consistent and repeatable errors that arise from a flaw in the equipment, experimental design, or observation method.
- Term
Random Error
- Meaning
Unpredictable variations in measured data that are not easily controlled or eliminated, often due to unknown and unpredictable changes in the measurement system.
- Term
Transducer
- Meaning
A device that converts one form of energy into another, typically converting a physical quantity (e.g., temperature, pressure) into an electrical signal.
Learning objectives
Understand the operating principles, construction, and characteristics of various analog and digital measuring instruments.
Analyze the sources of errors in measurements and apply methods for their reduction and compensation.
Select appropriate measuring instruments and techniques for specific electrical parameter measurements.
Apply bridge methods for precise measurement of resistance, inductance, and capacitance.
Interpret readings from DVMs and analyze waveforms using a CRO.
Understand the role and application of instrument transformers.
Formulae
- Name
PMMC Deflecting Torque
- Note
N = number of turns, B = flux density, I = current, A = coil area. For DC measurements.
- Expression
Td = NBIA
- Name
Moving Iron Deflecting Torque
- Note
I = RMS current, L = inductance, θ = deflection. For AC/DC RMS measurements.
- Expression
Td = (1/2)I²(dL/dθ)
- Name
Electrodynamometer Wattmeter Torque
- Note
Vp = potential coil voltage, Ic = current coil current, φ = phase angle between Vp and Ic. For AC/DC power.
- Expression
Td = Vp Ic cosφ
- Name
Wheatstone Bridge Balance Condition
- Note
For measuring medium resistance.
- Expression
R₁R₄ = R₂R₃
- Name
Kelvin Double Bridge for Low Resistance
- Note
For measuring low resistance (typically < 1 Ohm).
- Expression
Rₓ = (R₁/R₂)Rstd
- Name
Maxwell Bridge for Inductance
- Note
For measuring inductance with a low Q-factor (Q < 10).
- Expression
Lₓ = R₂R₃C₄
- Name
Hay Bridge for Inductance
- Note
For measuring inductance with a high Q-factor (Q > 10).
- Expression
Lₓ = (R₂R₃C₄) / (1 + (ωC₄R₄)²)
- Name
Schering Bridge for Capacitance
- Note
For measuring capacitance and dissipation factor.
- Expression
Cₓ = (R₂/R₁)C₃
- Name
Ammeter Shunt Resistance
- Note
Rm = meter resistance, n = range multiplier (Itotal / Im).
- Expression
Rsh = Rm / (n-1)
- Name
Voltmeter Multiplier Resistance
- Note
Rm = meter resistance, n = range multiplier (Vtotal / Vm).
- Expression
Rse = Rm (n-1)
- Name
Energy Meter Constant
- Note
Relates disk revolutions to consumed energy.
- Expression
K = (Number of revolutions) / (Energy in kWh)
Prerequisites
Basic Electrical Engineering (Ohm's Law, Kirchhoff's Laws, AC/DC circuit analysis, network theorems).
Basic knowledge of magnetic circuits and electromagnetic induction.
Fundamentals of Analog Electronics (e.g., op-amp basics for DVMs).
Common mistakes
Confusing the application of PMMC (DC only) and MI (AC/DC) instruments.
Incorrectly identifying the appropriate bridge for specific R, L, or C measurements, especially for inductance bridges based on Q-factor.
Neglecting the loading effect of instruments on the circuit being measured.
Errors in calculating shunt and multiplier resistances for range extension.
Misinterpreting the sources and types of measurement errors.
Not understanding the difference between accuracy and precision.
Keywords
PMMC
MI
Electrodynamometer
Wattmeter
Energy Meter
Wheatstone Bridge
Kelvin Bridge
Maxwell Bridge
Hay Bridge
Schering Bridge
Potentiometer
Current Transformer
Potential Transformer
DVM
CRO
Accuracy
Precision
Error
Transducer
Measurement
Practice preview
What is the purpose of a multiplier in a voltmeter?…
medium
A PMMC instrument is used for measuring DC quantities. What is the primary reason for this?…
medium
A Wheatstone bridge is used to measure:…
easy