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Power AND ENERGY Measurement The measurement of the integral, with respect to time, of the power in an electric circuit. The absolute unit of measurement of electrical energy is the joule, or the charge in coulombs times the potential difference in volts. The joule, however, is too small (1 watt-second) for use in commercial practice, and the more commonly used unit is the watt-hour (3.6 × 103 joules). The most common measurement application is in the utility field. Basically, measurements of electric energy may be classified into two categories, directcurrent power and alternating-current power. The fundamental concepts of measurement are, however, the same for both. There are two types of methods of measuring electrical energy: electric instruments and timing means, and electricity meters. Electric instruments and timing means make use of conventional procedures for measuring electric power and time. Typical methods are listed below: 1. Measurement of energy on a direct-current circuit by reading the line voltage and load current at regular intervals over a measured period of time. 2. Measurement of energy on a direct-current circuit by controlling the voltage and current at constant predetermined values for a predetermined time interval. 3. Measurement of energy on an alternating-current circuit by reading the watts input to the load at regular intervals over a measured period of time. 4. Measurement of energy on an alternating-current circuit by controlling the voltage, current, and watts input to the load at constant predetermined values. 5. Measurement of energy by recording the watts input to the load on a linear chart progressed uniformly with time. Electricity meters are the most common devices for measuring the vast quantities of electrical energy used by industry and the general public. The same fundamentals of measurement apply as for electric power measurement, but in addition the electricity meter provides the time-integrating means necessary for electric energy measurement. A single meter is sometimes used to measure the energy consumed in two or more circuits. However, multistator meters are generally required for this purpose. Watt-hour meters are generally connected to measure the losses of their respective current circuits. These losses are extremely small compared to the total energy being measured and are present only under load conditions. Watt-hour meters used for the billing of residential, commercial, and industrial loads are highly developed devices. The measurement of the time rate at which electrical energy is being transmitted or dissipated in an electrical system. The potential difference in volts between two points is equal to the energy per unit charge (in joules/coulomb) which is required to move electric charge between the points. Since the electric current measures the charge per unit time (in coulombs/second), the electric power p is given by the product of the current, i and the voltage, v (in joules/second = watts) Representation of electric power: The measurement of electric power is calculated by the ratio between the work performed by the time. That is, the measure of electric power is Power= Work done/Time Consider a current I passes through a conductor having the resistance R. The potential difference is V for time t. Then the electric power measure is Unit of W: joules(J) Unit of time: second(s) Therefore the unit of electric power: J/s or watts(W) P = (VIt)/t =V.I (joule second-1 or watt) We know the Ohm’s law: V=IR P=V.I=IR.I=I2R; P=V2/R where I = V/R Thus the measurement of electric power is P=V.I=I2R=V2/R Thus we can understand that the potential difference of 1 volt causes a current of 1 ampere then the electric power is 1 watt. Some large unit used in electric power: kilowatt: 1kilowatt=1000W megawatt:1megawatt=1000000W. The unit used in electricity meter at homes are kilowatthours(kWh). 1kWh = 3.6 x 106J Example:1 The work done by a heater is 100 joules for time 4 seconds. Find out the electric power of the heater. Solution: Given, Work done by a heater (W)=100 joule Time taken by a heater (t)=4 seconds Therefore the electric power of the heater P = W/t =100/4 =25 watt Example:2 The electric power of the electrical bulb is 50 watt. Then at how much time required to the electrical bulb to performed the work of 150 joules. Solution: Given, Electric power (P)=50 watt or 50 joules/second Work done by a bulb (W)=150 joules We know that P=W/t t=W/P = 150/50 Time t = 3 seconds The measurement of power in a dc circuit can be carried out by simultaneous measurements of voltage and current by using standard types of dc voltmeters and ammeters. In ac circuits the phase difference between the voltage and current precludes use of the voltmeter-ammeter method unless the load is known to be purely resistive. When this method is applicable, the instrument readings lead directly to average power since ac voltmeters and ammeters are always calibrated in rms values. In power-frequency circuits the most common instrument for power measurement is the moving-coil, dynamometer wattmeter. This instrument can measure dc or ac power by carrying out the required multiplication and averaging on a continuous analog basis. The instrument has four terminals, two for current and two for voltage, and reads the average power directly. It can be built with frequency response up to about 1 kHz. A special meter movement designed especially for power measurement is called the dynamometer movement, and is similar to a D'Arsonval or Weston movement in that a lightweight coil of wire is attached to the pointer mechanism. However, unlike the D'Arsonval or Weston movement, another (stationary) coil is used instead of a permanent magnet to provide the magnetic field for the moving coil to react against. The moving coil is generally energized by the voltage in the circuit, while the stationary coil is generally energized by the current in the circuit. A dynamometer movement connected in a circuit looks something like this: The top (horizontal) coil of wire measures load current while the bottom (vertical) coil measures load voltage. The (moving) voltage coil of a dynamometer is typically connected in series with a range resistor so that full load voltage is not applied to it. The (stationary) current coil of a dynamometer may have precision shunt resistors to divide the load current around it. With custom-built dynamometer movements, shunt resistors are less likely to be needed because the stationary coil can be constructed with as heavy of wire as needed without impacting meter response, unlike the moving coil which must be constructed of lightweight wire for minimum inertia. Early wattmeter on display at the Historic Archive and Museum of Mining in Pachuca, Mexico.