Download Resistors, Capacitors, and Inductors in AC Circuits

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 –
termed 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
the 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
voltage 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 that 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 current 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 efficiently 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 to 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=I2R) = 7500 Watt 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 Watt,
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. While 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.