YOKOGAWA WT500 - Page 340

App-20
IM 760201-01E
Series RLC Circuits
The equation below expresses the voltage relationships when resistance R
S
[
Ω
],
inductance L [H], and capacitance C [F] are connected in series.
U = (URS)
2
+ (UL – UC)
2
= (IRS)
2
+ (IXL – IXC)
2
= I (RS)
2
+ (XL – XC)
2
= I RS
2
+ XS
2
I =
U
RS
2
+ XS
2
, φ = tan
–1
XS
RS
RS
I
URS
I
L
UL
C
UC
U
UC
UL
U
U
RS
φ
The relationship between resistance R
S
, reactance X
S
, and impedance Z is expressed by
the equations below.
Z = RS
2
+ XS
2
XS = XL – XC
Parallel RLC Circuits
The equation below expresses the current relationships when resistance R
P
[
Ω
],
inductance L [H], and capacitance C [F] are connected in parallel.
I= (IRP)
2
+ (IL–IC)
2
=
U =
IRPXP
RP
2
+ XP
2
, φ = tan
–1
RP
XP
RP
U
2
+
XL
U
–
XC
U
2
=
RP
1
2
+
XL
1
–
XC
1
2
U =
RP
1
2
+
XP
1
2
U
RP
L
C
I
I
RP
IL
IC
U
U
IC
IL
I
I
RP
φ
The relationship between resistance R
P
, reactance X
P
, and impedance Z is expressed by
the equations below.
Z =
RPXP
RP
2
+ XP
2
XP =
XLXC
XC – XL
Appendix 3 Power Basics (Power, harmonics, and AC RLC circuits)