Download Lecture 4 - UniMAP Portal

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.