AC resistor circuits
If we were to plot the current and
voltage for a very simple AC circuit consisting of a source and a
resistor, it would look something like this:
Because the resistor allows an amount of
current directly proportional to the voltage across it at all periods of
time, the waveform for the current is exactly in phase with the waveform
for the voltage. We can look at any point in time along the horizontal
axis of the plot and compare those values of current and voltage with
each other (any "snapshot" look at the values of a wave are referred to
as instantaneous values, meaning the values at that instant
in time). When the instantaneous value for voltage is zero, the
instantaneous current through the resistor is also zero. Likewise, at
the moment in time where the voltage across the resistor is at its
positive peak, the current through the resistor is also at its positive
peak, and so on. At any given point in time along the waves, Ohm's Law
holds true for the instantaneous values of voltage and current.
We can also calculate the power
dissipated by this resistor, and plot those values on the same graph:
Note that the power is never a negative
value. When the current is positive (above the line), the voltage is
also positive, resulting in a power (p=ie) of a positive value.
Conversely, when the current is negative (below the line), the voltage
is also negative, which results in a positive value for power (a
negative number multiplied by a negative number equals a positive
number). This consistent "polarity" of power tells us that the resistor
is always dissipating power, taking it from the source and releasing it
in the form of heat energy. Whether the current is positive or negative,
a resistor still dissipates energy.
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