Bridges and Measurement of Power and Energy
Wheatstone, Kelvin double, Maxwell, Hay, Anderson, Schering and Wien bridges, wattmeter methods for single and three-phase power, energy meters, and potentiometers.
Bridges measure R, L and C by balancing; wattmeters and energy meters measure power and energy.
DC bridges
- Wheatstone bridge: balance when P/Q = R/S, so the unknown R = (P/Q) S. Best for medium resistances (1 Ω to 100 kΩ).
- Kelvin double bridge: low resistances (below 1 Ω), eliminates lead and contact resistance.
- Megger / loss of charge method: very high resistances (insulation).
AC bridges
Balance needs both magnitude and phase: Z₁ Z₄ = Z₂ Z₃ (two equations).
| Bridge | Measures | Notes |
|---|---|---|
| Maxwell's inductance–capacitance | Medium-Q inductors (1 < Q < 10) | Compares L with a standard C |
| Hay's | High-Q inductors (Q > 10) | |
| Anderson's | Inductance precisely, over a wide range | Modified Maxwell |
| Schering | Capacitance and dissipation factor (insulation) | High voltage use |
| Wien | Frequency (and capacitance) | f = 1/(2πRC) for equal arms |
| De Sauty | Capacitance (lossless) | Simple |
Maxwell L–C bridge balance: L_x = R₂ R₃ C₁, R_x = R₂R₃/R₁.
Power measurement
- Electrodynamometer wattmeter: current coil in series, pressure coil across the load; reads V I cos φ.
- Three-phase power: two-wattmeter method for three-wire loads: P = W₁ + W₂ and tan φ = √3(W₁ − W₂)/(W₁ + W₂). One wattmeter reads zero at pf 0.5 and negative below it.
- Reactive power of a balanced load from one wattmeter with its pressure coil across the other two lines: Q = √3 × reading.
Energy meters
- Induction-type energy meter (older): an aluminium disc driven by eddy currents; braked by a permanent magnet. Meter constant K = revolutions per kWh.
- Adjustments: light load (friction) compensation, lag adjustment (for correct power factor), creep prevention (holes in the disc).
- Electronic (static) meters are now standard.
- Percentage error = (energy recorded − true energy)/true energy × 100.
Potentiometers
A DC potentiometer measures voltage by comparing with a standard cell at null (no current is drawn from the unknown), so it is very accurate; it is also used to calibrate meters.
Worked example
A Wheatstone bridge balances with P = 100 Ω, Q = 1000 Ω and S = 470 Ω.
- R = (P/Q) S = 0.1 × 470 = 47 Ω.
Practice
An energy meter has a constant of 600 rev/kWh. A 2 kW load runs for 30 minutes. How many revolutions should the disc make?
Show answer and explanation
Answer: 600Energy = 2 × 0.5 = 1 kWh, so 600 revolutions.
The same meter actually makes 612 revolutions. What is its percentage error?
Show answer and explanation
Answer: 2Error = (612 − 600)/600 × 100 = +2% (the meter runs fast).
A Wien bridge has R = 10 kΩ and C = 10 nF in both arms. At what frequency (Hz) does it balance? (Give 1 decimal place.)
Show answer and explanation
Answer: 1591.5f = 1/(2πRC) = 1/(2π × 10⁻⁴) = 1591.5 Hz.
Which bridge is best for measuring the capacitance and loss angle of a cable's insulation?
Show answer and explanation
Answer: CThe Schering bridge measures capacitance and dissipation factor, often at high voltage.