But for a high-frequency signal, the capacitor’s impedance is very
small, and it acts like a zero-impedance, easy path into which the
current is diverted.
The main things to be careful about with impedance are that
(1) the concept only applies to a circuit that is being driven sinu-
soidally, (2) the impedance of an inductor or capacitor is frequency-
dependent.
Discussion Question
A Figure z on page 629 shows the voltage and current for a capacitor.
Sketch theq-tgraph, and use it to give a physical explanation of the
phase relationship between the voltage and current. For example, why is
the current zero when the voltage is at a maximum or minimum?
B Figure ac on page 630 shows the voltage and current for an inductor.
The power is considered to be positive when energy is being put into the
inductor’s magnetic field. Sketch the graph of the power, and then the
graph ofU, the energy stored in the magnetic field, and use it to give
a physical explanation of theP-tgraph. In particular, discuss why the
frequency is doubled on theP-tgraph.
C Relate the features of the graph in figure ac on page 630 to the story
told in cartoons in figure m/2-3 on page 620.10.5.8 Power
How much power is delivered when an oscillating voltage is ap-
plied to an impedance? The equationP = IV is generally true,
since voltage is defined as energy per unit charge, and current is
defined as charge per unit time: multiplying them gives energy per
unit time. In a DC circuit, all three quantities were constant, but
in an oscillating (AC) circuit, all three display time variation.A resistor
First let’s examine the case of a resistor. For instance, you’re
probably reading this book from a piece of paper illuminated by
a glowing lightbulb, which is driven by an oscillating voltage with
amplitudeVo. In the special case of a resistor, we know thatIand
V are in phase. For example, ifV varies asVocosωt, thenIwill be
a cosine as well,Iocosωt. The power is thenIoVocos^2 ωt, which is
always positive,^6 and varies between 0 andIoVo. Even if the time
variation was cosωtor sin(ωt+π/4), we would still have a maximum
power ofIoVo, because both the voltage and the current would reach
their maxima at the same time. In a lightbulb, the moment of
maximum power is when the circuit is most rapidly heating the
filament. At the instant whenP= 0, a quarter of a cycle later, no
current is flowing, and no electrical energy is being turned into heat.
Throughout the whole cycle, the filament is getting rid of energy by(^6) A resistor always turns electrical energy into heat. It never turns heat into
electrical energy!
632 Chapter 10 Fields