electricity and magnetism 29 alternating currents and power transmission chapter 29 alternating...

Electricity and MagnetismElectricity and Magnetism

29 Alternating Currents and Power Transmission

Chapter 29

Alternating Currents and Power Transmission

29.1 Alternating current

• In a direct current (d.c.) circuit, electric current flows in one

direction only.

Alternating currents and alternating voltages

• In an alternating current (a.c.) circuit, current reverses its

direction periodically.• In general, a.c. are produced by alternating e.m.f.s (voltages)

from a.c. sources.

Square waveform Sinusoidal waveform

• A sinusoidal alternating voltage can be expressed as

where V0 is its peak value and is its angular frequency.

• The angular frequency is

related to the frequency f

and the period T of the

voltage by

V = V0 sin t

π2π2

Resistive circuit

• In a purely resistive circuit,

V and I are in phase.

Example 29.1 Checkpoint (p.418) O

V = V0 sin t I = I0 sin t

• However, what we really concern is the average power of an

a.c. supplied to a resistive load, which is given by

where the symbol denotes the time-average of the

enclosed quantity.

Root-mean-square (r.m.s.) values

Experiment 29.1

RIRIP 22

• Applying P = VI, for sinusoidal

voltage and current, the

instantaneous power supplied to

the load is

P = V0I0 sin2t

• For a sinusoidal voltage, we have

• The root-mean-square (r.m.s.)

value of a current I is defined as

• Hence, for sinusoidal voltages, we have .

• Since , we have

2rms II

tII sin20

RIP 2rms

R.m.s. values of alternating currents of square waveform

• In other words,

• The average power can be expressed in the following forms:

• For sinusoidal alternating currents and voltages, we have

The root-mean-square (r.m.s.) value of an a.c. is the

steady d.c. which delivers the same average power

as the a.c. to a resistive load.

RIP 2rms

VP rms rmsrmsIVP

Example 29.2Checkpoint (p.423) O

29.2 Transformer

• A transformer is a device that can change the value of an

alternating voltage.

A transformer for notebook computers

Substations contain a lot of transformers.

• A change in current through a coil induces a voltage in

another nearby coil due to the change in magnetic field

through the latter coil.• This effect is called mutual induction.

Structure and working principle of a simple transformer

• The primary coil of a transformer is connected to an a.c.

source and the secondary coil gives the output voltage.• If the magnetic flux through each turn of the coils in a

transformer is the same, there is perfect flux linkage (i.e. no

flux leakage) between the coils.

• The voltage ratio and turns ratio of a transformer, with perfect

flux linkage and negligible coil resistance, are related by

Voltages and currents in transformers

Experiment 29.2

• Apply Faraday’s law, the alternating magnetic flux through

the coils induce e.m.f.s in the coils.

• With the iron core, the magnetic flux through each turn of the

two coils is the same.

• For a step-up transformer, Ns > Np, and so Vs > Vp.

• For a step-down transformer, Ns < Np, and so Vs < Vp.

• The efficiency of a transformer can be expressed as

% 100% 100powerinput

poweroutput efficiency

Transformer

• An ideal transformer has 100% efficiency. For such a

transformer, we have

• Since , we have

• Hence, for an ideal transformer, whenever the voltage is

stepped up (or stepped down), the current through the

secondary coil decreases (or increases) by the same factor.

Example 29.3Checkpoint (p.431) O

Example 29.4

• Transformers have very high efficiency, but are never ideal.

Energy loss in transformers and practical transformer designs

improvements made in practical transformers

reasons for energy loss

use high-qualitymagnetic materials tomake the core

continuous magnetization and demagnetization of the iron core

use thick copper wires to make the coils

resistance in the coils

improvements made in practical transformers

reasons for energy loss

use a laminated coreeddy currents in the iron core

Checkpoint (p.433) O

29.3 Transmission and distribution of electricity

• One of the problems in

transmitting electricity is the

power loss in the transmission

lines due to the heating effect of

current.

Overhead transmission lines

Power loss in transmission lines

• If a transmission line carries a current I and has a resistance

R, the power dissipated as heat is given by

• The lower the current, the lower

the power dissipated.• Using transformers, a.c. voltage

can be stepped up easily and

efficiently, and the current can be

stepped down accordingly.• Hence, alternating current is

used to transmit mains electricity

in order to reduce the power

P = I2R

Experiment 29.3

Overhead transmission lines

Example 29.5

• A grid system is a transmission and distribution network of

mains electricity.

Grid system in Hong Kong

• The voltage of the electricity generated at a power station is

stepped up before transmission and stepped down

successively at substations in populated areas.

Checkpoint (p.441) O

Schematic diagram of the grid system in Hong Kong

Birds on transmission lines

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