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 simply and directly
resists the flow of electrons at all periods of time, the waveform for
the voltage drop across the resistor is exactly in phase with the
waveform for the current through it. 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
current is zero, the instantaneous voltage across the resistor is also
zero. Likewise, at the moment in time where the current through the
resistor is at its positive peak, the voltage across 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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