Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

40 CHAPTER 2
Figure 2-18. A circuit having a capacitance C and a
resistance R in series with a voltage source V.
The loss tangent is a measure of energy absorption by a medium through which an
electromagnetic wave passes; energy absorption by the medium is directly proportional
to the loss tangent. The loss tangent is defined as
Loss tangent =
conduction current
displacement current
(2.64)
Conduction current is the ordinary current that consists of a flow of electrons across
a potential difference in a circuit. Since no dielectric material is a perfect insulator,
some small conduction current will flow through any insulating material under the
influence of a potential difference. Displacement is a concept proposed by Maxwell
to account for the apparent flow of current through an insulator—even a perfect
insulator—under the action of a changing voltage.
Consider the circuit shown in Figure 2-18, a capacitor (whose dielectric is a perfect
insulator), a resistor, a switch, and a battery are connected in series. While the switch
is open, plate a of the capacitor is at the same potential as the positive terminal of
the battery to which it is connected through the resistor. When the switch is closed,
plate b of the capacitor is connected to the negative pole of the battery, and the
capacitor begins to charge under the influence of the potential across the plates.
Since the dielectric in this circuit is a perfect insulator, clearly no current can flow
through the dielectric. However, connecting the plates of the capacitor to the battery
terminals causes electrons to pile up on the negative plate and to be drained off from
the positive plate. That is, electrons flow onto the plate connected to the negative
terminal and flow from the other plate to the positive terminal until an equilibrium
is reached when no more charge flows. Thus, during the time that the capacitor is
charging, the circuit behaves as if current were flowing through every portion of the
circuit, including the dielectric. This apparent current flowing through the dielectric
is called the displacement current. Since no real dielectric is a perfect insulator, there
always is a conduction current through the dielectric in addition to the displacement
current. Furthermore, since a conduction current is always accompanied by energy
loss through joule heating, there always is some loss of energy when a dielectric is
placed in an electric field.
While the capacitor is charging, the displacement current in the circuit is given
by
i = V
R e −t/RC , (2.65)
and the voltage across the capacitor is given by
VC = V (1 − e −t/RC ) (2.66)