boylistad

ƒ r
The magnitude of the current IC can then be determined using Ohm’s
law, as follows:
IC � �
Substituting XC � XL when Ql ≥ 10,
Q
IC � �IT � IT 2 Q l
�
Ql
2 l
—
� X
IT Q
L
�
R
2 ITQ lRl �
XL
2 VC lRl � �
XC XC
and IC � QlIT Ql ≥ 10 (20.56)
revealing that the capacitive current is Q l times the magnitude of the
current entering the parallel resonant circuit. For large Q l, the current I C
can be significant.
A similar derivation results in
Conclusions
I T
Z Tp = R p = Q l 2 Rl
I L � Q lI T
Q l ≥ 10
(20.57)
The equations resulting from the application of the condition Q l ≥ 10
are obviously a great deal easier to apply than those obtained earlier. It
is, therefore, a condition that should be checked early in an analysis to
determine which approach must be applied. Although the condition
Q l ≥ 10 was applied throughout, many of the equations are still good
approximations for Q l < 10. For instance, if Q l � 5, X Lp � (X L/Q 2 l) �
X l � (X L/25) � X L � 1.04X L, which is very close to X L.Infact,for
Q l � 2, X Lp � (X L/4) � X L � 1.25X L, which agreeably is not X L, but it
is only 25% off. In general, be aware that the approximate equations
can be applied with good accuracy with Q l < 10. The smaller the level
of Q l, however, the less valid the approximation. The approximate equations
are certainly valid for a range of values of Q l < 10 if a rough
approximation to the actual response is desired rather than one accurate
to the hundredths place.
20.11 SUMMARY TABLE
RP XL XC VC –
FIG. 20.31
Establishing the relationship between I C and I L and the current I T.
In an effort to limit any confusion resulting from the introduction of f p
and f m and an approximate approach dependent on Q l, summary Table
20.1 was developed. One can always use the equations for any Q l,but
I L
l
I C
+
SUMMARY TABLE ⏐⏐⏐ 911