Download Chapter 21

AC Current


An AC circuit consists of a combination of
circuit elements and an AC generator or
source
The output of an AC generator is sinusoidal
and varies with time according to the
following equation

V = V0 sin 2ƒt



V is the instantaneous voltage
V0 is the maximum voltage of the generator
ƒ is the frequency at which the voltage changes, in Hz
AC Generators

Basic operation of the
generator




As the loop rotates, the
magnetic flux through it
changes with time
This induces an emf and
a current in the external
circuit
The ends of the loop are
connected to slip rings
that rotate with the loop
Connections to the
external circuit are made
by stationary brushed in
contact with the slip rings
AC Generators

The emf generated by
the rotating loop can
be found by
ε = 2 (B ℓ v)


ε = εmax when loop is
parallel to the field
ε = 0 when when the
loop is perpendicular
to the field
AC Generators, final

Original AC voltage

Increase B, Area, or
# of turns

Increase frequency
of rotation
Resistor in an AC Circuit



The graph shows the
current through and
the voltage across
the resistor
The current and the
voltage reach their
maximum values at
the same time
The current and the
voltage are said to
be in phase
rms Current and Voltage

The rms current is the direct current that
would dissipate the same amount of
energy in a resistor as is actually
dissipated by the AC current
Irms

=
I
Io = peak or max current
o
2
Alternating voltages can also be discussed
in terms of rms values
V rms
=
V0
2
Vo = peak voltage
Ohm’s Law in an AC Circuit

rms values will be used when discussing
AC currents and voltages


AC ammeters and voltmeters are designed to
read rms values
Ohm’s Law for a resistor, R, in an AC
circuit

ΔVrms = Irms R
Example
An AC voltage source has a peak output of 200V.
If the source is connected to a 100W resistor, find
the rms current.
V rms =
I
rms
=
V0
2
V rms
R
What is the max current?
=
200 V
2
= 141 V
= 141 V / 100 W = 1.41 A
Irms =
I
o
2
1.41 A =
I
o
2
Io = 2A
Transformers
Transformers


An AC transformer
consists of two coils
of wire wound around
a core of soft iron
The side connected to
the input AC voltage
source is called the
primary and has N1
turns
Schematic symbol for a transformer
Shell type
Transformers, 2

The other side, called the secondary, is
connected to a resistor and has N2 turns

Current passing through the primary
coil induces a magnetic field (magnetic
flux) in the iron core.
The magnetic flux is
transmitted to the other
side and induces a
voltage in the secondary coil.
Transformers, 3

The voltages are related by
Vp N p
=
Vs N s
Where:
Vp = Primary coil voltage
Vs = Secondary coil voltage
Np = # of turns of wire in the Primary coil
Ns = # of turns of wire in the Secondary coil
Transformers, 4
Vp N p
=
Vs N s
When
Ns > Np, the transformer is
referred to as a step up transformer
(more voltage out)
When Np > Ns, the transformer is
referred to as a step down
transformer (less voltage out)
*This
works because there is a direct
relationship between the # of turns
and the induced voltage

=N
t
Transformer, 5

The power input into the primary equals the
power output at the secondary

I1ΔV1 = I2ΔV2


You don’t get something for nothing (conservation of
energy)
This assumes an ideal transformer

In real transformers, power efficiencies typically range
from 90% to 99%
Electrical Power Transmission

When transmitting electric power over long
distances, it is most economical to use high voltage
and low current


Minimizes I2R power losses (P = VI = I2R)
In practice, voltage is stepped up to about 230, 000
V at the generating station and stepped down to
20 000 V at the distribution station and finally to
120 V at the customer’s utility pole