User`s guide
EE PRO for TI -89, 92 Plus
Equations - RL and RC Circuits
43
21.5 RL Series to Parallel
The equations in this topic show the equivalence relationship
between a series RL circuit (Rs and Ls) and its parallel equivalent
circuit, Rp, Lp. The first equation translates the frequency, f,
to its radian frequency,
ω
. The second equation specifies the
quality factor Qs for Rs and Ls. The third and fourth equations
define the values of Rp and Lp in terms of Rs, Ls and
ω
. The fifth
equation computes Qp in terms of Rp, Lp and
ω
. The sixth and seventh equations calculate Rs and Ls in terms of
Rp, Lp and
ω
. The eighth and ninth equations compute Rp and Lp in terms of Rs, Ls and Qs. The last two of
equations calculate Rs and Ls in terms of Rp, Lp and Qp.
ωπ
=⋅⋅2
f
Eq. 21.5.1
Qs
Ls
Rs
=
⋅
ω
Eq. 21.5.2
Rp
Rs Ls
Rs
=
+⋅
222
ω
Eq. 21.5.3
Lp
Rs Ls
Ls
=
+⋅
⋅
222
2
ω
ω
Eq. 21.5.4
Qp
Rp
Lp
=
⋅
ω
Eq. 21.5.5
Rs
Lp Rp
Rp Lp
=
⋅⋅
+⋅
ω
ω
22
222
Eq. 21.5.6
Ls
Rp Lp
Rp Lp
=
⋅
+⋅
2
222
ω
Eq. 21.5.7
Rp Rs Qs
=⋅+1
2
ch
Eq. 21.5.8
Lp Ls
Qs
=⋅+
F
H
G
I
K
J
1
1
2
Eq. 21.5.9
Rs
Rp
Qp
=
+1
2
Eq. 21.5.10
Ls
Qp Lp
Qp
=
⋅
+
2
2
1
Eq. 21.5.11
Example 21.5 -
A 24_mH inductor has a quality factor of 5 at 10000_Hz. Find its series resistance and the
parallel equivalent circuit parameters.