AC Circuits and Transformer Notes

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5 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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Resistors, Capacitors, and Inductors in AC Circuits

This paper is not intended to give sufficient information to do circuit analysis or design on ac
circuits

but rather to give an indication of how the basic circuit elements of resistors, capacitors,
and
inductors

can
CONTROL
the voltage and current in ac circuits.

It is important to remember that ac circuits are continuously changing sine waves of current and

voltage. Unless informed otherwise it is easy to imagine that these sine waves are “in step


ter
med

in phase” everywhere in these circuits. This is not true in general and there are ways to
control the

relative phase of the current and voltage signals to the advantage of the
experimenter. The website

mentioned below has
animations
of how the signals
behave.

Resistors:
Ohm’s Law holds for ac circuits in the most
obvious

fashion and the voltage signal and the current signal
are in phase

at every instant
within
and
across
the resistor.
The ability to

control the current flow is available regardless of
th
e frequency of

the signal. The diagram taken from the URL

http://www.physclips.unsw.edu.au/site_map.htm#AC

Portrays
the two quantities in phase (maximum of one occurs at

the
same time as

the maximum of the other).

Capacitors:
While there is a relationship similar to Ohm’s law
for capacitors the voltage across the

capacitors terminals is
not in phase with the current through the

capacitor.
Remember that a capacitor will completely block
the flow of

dc current and as current goes to zero the capacitor achieves

maximum voltage across its terminals. In ac circuits the
phase angle

between the current and voltage values for
capacitors is 900 out of

phase. The current is said to
lead
the
voltag
e and the maximum in the

current sine curve occurs ¼
of a cycle before the voltage signal

maximizes. In the diagram at the right notice that the current
is zero at

time = 0 but the voltage zero occurs at a later time. One important thing to remember
is tha
t

capacitors can be used to change
(control)
the relative phase between the current and
voltage in ac

circuits. This may be useful at times.

Inductors:
Inductors (coils) are in some sense the opposite of
capacitors in ac circuits. While

capacitors tend to

block current
flow at low frequencies and shift the phase of

the current to
lead the phase of the voltage, inductors tend to block the flow
of

current at high frequencies and to shift the phase of current
behind the phase of

the voltage. The inductor can
be
used to
control the relative phase and

amplitude of current and
voltage signals
in ac circuits.

Other circuit elements
: There are other circuit elements in ac circuits that assist in controlling
the

phase, amplitude, and shape of ac signals but one can
see the potential for control from
these three

devices alone.


The Transformer and Power Transmission

The transformer's ability to step AC voltage up or down with ease gives AC an
advantage unmatched

by DC in the realm of power distribution shown in the
figure
below. When transmitting electrical power

over long distances, it is far more efficient to
do so with stepped
-
up voltages and stepped
-
down

currents (smaller
-
diameter wire with
less resistive power losses), then step the voltage back down

and the cur
rent back up
for industry, business, or consumer use.


Transformers enable efficient long distance high voltage transmission of electric energy.

Transformer technology has made long
-
range electric power distribution practical.
Without the ability

to effic
iently step voltage up and down, it would be cost
-
prohibitive to
construct power systems for

anything but close
-
range (within a few miles at most) use.

Example Calculation: Power Considerations

Assume that the resistance of the wires from the power plant t
o your house is 100
Ohms, that your

average power usage is 1,000 watts, and that the voltage needed is
110
-
120 volts. In rough numbers

the average current used is (I = P/V) 8.7 amps.

Power loss using direct current transferred at 115 volts


(P=I
2
R) =
7500

W
att
or more
than is used

in the house. Most of the energy is lost in the transmission line.

Power loss using
AC

with current transferred at 10,000 volts and stepped down with a
transformer.

The current will be 0.1 amp and the power lost in the lines is
1.15
W
att,
which may be tolerable.

Another disadvantage
of
DC

is that either every item in the house must use the same
voltage

(remember that transformers in the computer will not work) or separate lines
must be used for each

voltage used in the house.
Whi
le all plug
-
in items

in the house
use 115 volts
AC
, many have a transformer

inside to adjust

to

the voltage

requirements

for that
device
.