Measurement: Process of comparing unknown quantity with standard

Accuracy: Closeness of measured value to true value

Precision: Repeatability of measurements

Resolution: Smallest change that can be detected

Sensitivity: Change in output per unit change in input

Linearity: Proportional relationship between input and output

Hysteresis: Different output for same input (loading vs unloading)

Systematic Errors: Constant deviation (calibration, environmental)

Random Errors: Unpredictable variations

Gross Errors: Human mistakes, equipment failure

Absolute Error: \(\Delta A = A_m - A_t\)

Relative Error: \(\dfrac{\Delta A}{A_t} \times 100\%\)

Limiting Error: Maximum possible error

Percentage Error: \(\dfrac{\Delta A}{A_t} \times 100\%\)

Range: Minimum to maximum input values

Span: Algebraic difference between maximum and minimum

Threshold: Minimum input to produce output change

Dead Zone: Range where output remains constant

Drift: Change in output over time with constant input

Repeatability: Closeness of successive measurements

Reproducibility: Ability to reproduce results under different conditions

Moving Coil Voltmeter: High series resistance

Multiplier: \(R_m = R_g(n-1)\) where \(n = \dfrac{V}{V_g}\)

Digital Voltmeter: High input impedance, accurate

Potentiometer: Null deflection method, high accuracy

Loading Effect: Meter resistance affects circuit

Voltage Divider: For range extension

Input Impedance: Should be much higher than source resistance

Moving Coil Ammeter: Low series resistance

Shunt: \(R_s = \dfrac{R_g}{n-1}\) where \(n = \dfrac{I}{I_g}\)

Current Transformer: For high currents, isolation

Hall Effect Sensor: Non-contact measurement

Shunt Types: Manganin (low temp coefficient)

Shunt Box: Multiple range selection

Burden: Voltage drop across shunt

Ammeter-Voltmeter Method: \(R = \dfrac{V}{I}\)

Wheatstone Bridge: \(R_x = \dfrac{R_2 R_3}{R_1}\) (balanced condition)

Kelvin Bridge: For low resistance (\(< 1\Omega\))

Megger: For high resistance and insulation

Ohmmeter: Self-contained, less accurate

Substitution Method: Replace unknown with known standard

Comparison Method: Direct comparison with standard

High Resistance: Guard ring method, megohmmeter

Medium Resistance: Wheatstone bridge (1\(\Omega\) to 1M\(\Omega\))

Low Resistance: Kelvin bridge, four-terminal method

Micro-ohmmeter: For very low resistance

Insulation Resistance: Megger, guard terminal

Earth Resistance: Fall-of-potential method

Moving Iron Instruments: RMS response, AC/DC

Rectifier Type: Average responding, RMS calibrated

True RMS: Thermal converters, accurate for distorted waves

Peak Reading: Diode peak detector circuits

Form Factor: \(\dfrac{\text{RMS}}{\text{Average}} = 1.11\) (sine wave)

Crest Factor: \(\dfrac{\text{Peak}}{\text{RMS}} = 1.414\) (sine wave)

Peak-to-Peak: \(V_{p-p} = 2V_{peak}\)

Attraction Type: Iron piece attracted to coil

Repulsion Type: Two iron pieces repel each other

Dynamometer: Two coils, one fixed, one movable

Induction Type: Rotating magnetic field principle

Thermocouple Type: Heat generated by current

Electrostatic: Electrostatic force between plates

Wattmeter: \(P = VI\cos\phi\) (single phase)

Two Wattmeter Method: \(P = W_1 + W_2\) (3-phase)

Reactive Power: \(Q = \sqrt{3}VI\sin\phi\)

Power Factor: \(\cos\phi = \dfrac{P}{VI}\)

Energy Meter: Induction type, kWh measurement

Apparent Power: \(S = VI\) (VA)

Power Triangle: \(S^2 = P^2 + Q^2\)

Direct Method: One wattmeter for resistive load

Wattmeter Connections: Voltage and current coils

Compensation: For wattmeter losses

Low Power Factor: Special connections required

Reactive Power: \(Q = VI\sin\phi\)

Power Factor Meter: Direct reading instrument

Balanced Load: \(P = \sqrt{3}V_L I_L \cos\phi\)

Two Wattmeter Method:

• \(P_1 = V_L I_L \cos(30^{\circ} - \phi)\)

• \(P_2 = V_L I_L \cos(30^{\circ} + \phi)\)

• \(P_{total} = P_1 + P_2\)

Reactive Power: \(Q = \sqrt{3}(P_1 - P_2)\)

Power Factor: \(\tan\phi = \dfrac{\sqrt{3}(P_1 - P_2)}{P_1 + P_2}\)

Three Wattmeter Method: For unbalanced loads

Star Connection: Neutral point available

Delta Connection: No neutral point

Blondel’s Theorem: (n-1) wattmeters for n-wire system

Power Factor Limits:

• \(\cos\phi > 0.5\): Both wattmeters positive

• \(\cos\phi = 0.5\): One wattmeter reads zero

• \(\cos\phi < 0.5\): One wattmeter negative

Maxwell’s Bridge: \(L_x = \dfrac{R_2 R_3 C_1}{1}\), \(R_x = \dfrac{R_2 R_3}{R_1}\)

Hay’s Bridge: For high Q coils

Anderson Bridge: Most accurate for medium Q

Owen Bridge: For high Q inductors

Resonance Method: \(L = \dfrac{1}{\omega^2 C}\)

Q-Factor: \(Q = \dfrac{\omega L}{R}\)

Schering Bridge: \(C_x = \dfrac{C_1 R_3}{R_2}\), \(\tan\delta = \omega C_1 R_1\)

Wien Bridge: For capacitance and frequency

De Sauty Bridge: For perfect capacitors

Resonance Method: \(C = \dfrac{1}{\omega^2 L}\)

Loss Angle: \(\delta\) represents dielectric loss

Dissipation Factor: \(D = \tan\delta\)

Balance Condition: \(Z_1 Z_3 = Z_2 Z_4\)

Magnitude Balance: \(|Z_1||Z_3| = |Z_2||Z_4|\)

Phase Balance: \(\phi_1 + \phi_3 = \phi_2 + \phi_4\)

Convergence: Bridge should balance quickly

Sensitivity: Change in detector for small unbalance

Wagner Earth: Eliminates stray capacitance effects

Maxwell: Inductance measurement (medium Q)

Hay: Inductance measurement (high Q)

Anderson: Inductance measurement (most accurate)

Owen: Inductance measurement (variable frequency)

Schering: Capacitance and loss angle

Wien: Frequency measurement

Robinson: Capacitance measurement

Induction Type: Most common for AC energy

Rotating Disc: Speed proportional to power

Energy: \(E = \int P \, dt\) (kWh)

Meter Constant: Energy per revolution

Creep: Slow rotation at no load

Friction: Compensation for bearing friction

Digital Meters: Electronic energy measurement

Calibration: Against standard wattmeter

Accuracy Class: 0.1, 0.2, 0.5, 1.0, 2.0

Light Load: Performance at 10% of full load

Full Load: Performance at 100% of full load

Unity Power Factor: Most accurate condition

Lagging Power Factor: Typical industrial condition

Temperature Effect: Compensation required

Multiplier: \(R_m = R_g(n-1)\)

Shunt: \(R_s = \dfrac{R_g}{n-1}\)

Wheatstone Bridge: \(R_x = \dfrac{R_2 R_3}{R_1}\)

Power (3-phase): \(P = \sqrt{3}V_L I_L \cos\phi\)

Two Wattmeter: \(\tan\phi = \dfrac{\sqrt{3}(W_1 - W_2)}{W_1 + W_2}\)

Maxwell Bridge: \(L_x = \dfrac{R_2 R_3 C_1}{1}\)

Form Factor: \(F.F = \dfrac{RMS}{Average}\)

Crest Factor: \(C.F = \dfrac{Peak}{RMS}\)

Schering Bridge: \(C_x = \dfrac{C_1 R_3}{R_2}\)

Q-Factor: \(Q = \dfrac{\omega L}{R}\)

Power Triangle: \(S^2 = P^2 + Q^2\)

Reactive Power: \(Q = \sqrt{3}(P_1 - P_2)\)

Common Topics: Bridge circuits, power measurement, AC/DC instruments

Numerical Problems: Shunt/multiplier calculations, bridge balance

Conceptual Questions: Instrument selection, measurement principles

Practice Areas: Two wattmeter method, AC bridges, energy meters

Time Management: Quick formula recall essential

Units: Always check units in calculations

Bridge Calculations: Balance conditions, unknown component values

Power Measurement: Three-phase power, power factor calculation

Instrument Selection: Appropriate instrument for specific measurement

Range Extension: Shunt and multiplier calculations

Energy Measurement: Meter constants, calibration

AC Quantities: RMS, average, peak relationships