The phase meter shows the effect of frequenc on the

FIGURE
16-16
The
"phase
meter" shows the effect of
frequenc!
on the phase angle of a circuit, The
"phase
meter" indicates the phase angle change between two voltages, V, and Vp. Since Vp
and I are in phase, this angle is the same as the angle between V, and L
Figure 16-17 uses
the impedancetriangle to illustrate the variations inX6, Z, and 0
as the frequency changes. Of course, R remains constant. The key point is that because X6'
varies inversely with the frequency, so also do the magnitude of the total impedance and
the phase angle. Example 16-4 illustrates this.
vrl
7 f
flGURE16-17
As the
frequency
increases, Xg decreases, Z decreases, and
0 ilecreases. Each
value of
frequency
can be visualized as
forming
a dffirent
impedance triangle.
Increasing
/
ft
Lc3
^c2
J 2
J 1
Phase meter
Phase meter
^cl

610 r RC CIRCUITS
SECTION 1 6-3
1. In a certain series RC circuit, Vn =
4 V, and Vc
=
6 V. What is the magnitude of the
REVIEW
source voltage?
2. In
Question
1, what is the phase angle between the source voltage and the current?
3. What is the phase difference between the capacitor voltage aad the resistor voltage
in a series RC circuit?
4. When the frequency of the applied voltage in a series RC circuit is increased, what
happens to the capacitive reactance? what happens to the magnitude of the total
impedance? What happens
to the phase angle?
EXAMPLE 16-4
For the series RC circuit in Figure 16-18, determine the magnitude of the total imped-
ance and the phase angle for each of the following values of input frequency:
(a) 10 kHz (b) 20 kHz (c)
30 kHz
FIGURE 16-18
Solution
(a) For/= 10kHz,
_ _ |
I
=
1.59 kQ
2nfC 2n(r0kHz)(Q.01 pF)
0.01
pF
z=f R\ x/z-tan-'lIt\
-
\ R /
=
@z-t"''(ffi)
=
r.ssr-sz.e. ko
Thus, Z= 1.88
kO and 0
=
-57.9'.
(b) Forf=20kHz,
"'=;rzo
**0o'
uo,
=
7e6 r2
z
=
@
Lan-,
(J9SP)
=
r.zz.-zs.s. ko
Thus, Z
=
1.28 kO and 0
= -38.5'.
(c) For/= 30 kHz,
x'=
t(30 kHhJl
,F)
=
531 o
z
=
@.2-tan-r(!11
I
\
=
t.tzt-zs.o" ko
Thus, Z= 1.13 kO and 0
=
-28.0".
Notice that as the frequency increases, X6, Z, and d decrease.
Related Prohlem Find the magnitude of the total impedance and the phase angle in
Figure 16-18 for
f
=
| kJlz.
I coverage of serics reuctive circuits continues in chapter 17, Part r, on page 664.

r
IMPEDANCE AND PHASE
ANGTE OF PARATTEL RC CIRCUITS
In this section, you will learn how to determine the impedance and phase angle of a
parallel RC circait. Also, capacitive susceptance and admittance of a parallel RC cir-
cuit are introduced,
After compkting this section, you should be able to
I Determine impedance and phase angle in a parallel RC circuit
.
Express total impedance in complex form
.
Define and calculate conductance, capacitive susceptance, and admittance
Figure l6-19 shows a basic parallel RC circuit connected to an ac voltage source.
FIGURE 16-19
Basic parallel RC circuit.
The expressionfor the total impedance is developed as follows, using the rules of
phasor algebra. Since there are only two components, the total impedance can be found
from the product-over-sum rule.
z
(R/0")dcz-90")
t =
R a x ,
By multiplying the magnitudes, adding the angles in the numerator, and converting the
denominator to polar form, we get
Rxcl(o"
-
90')
Z -
\/n\x'rz.--
(+)
611

612 r RC CIRCUITS