App-19
IM 760201-01E
Appendix
3
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App
Index
AC RLC Circuits
Resistance
The current i when an AC voltage whose instantaneous value u = U
m
sin
ω
t is applied
to load resistance R [
Ω
] is expressed by the equation below. I
m
denotes the maximum
current.
i
=
U
m
R
sin
ω
t
=
I
m
sin
ω
t
Expressed using rms values, the equation is I = U/R.
There is no phase difference between the current flowing through a resistive circuit and
the voltage.
R
I
U
U
I
Inductance
The current i when an AC voltage whose instantaneous value u = U
m
sin
ω
t is applied to a
coil load of inductance L [H] is expressed by the equation below.
i
=
U
m
X
L
sin
W
t –
sin
W
t –
P
2
=
I
m
P
2
Expressed using rms values, the equation is I = U/X
L
. X
L
is called inductive reactance
and is defined as X
L
=
ω
L. The unit of inductive reactance is
Ω
.
Inductance works to counter current changes (increase or decrease), and causes the
current to lag the voltage.
L
I
U
U
I
P
2
Capacity
The current i when an AC voltage whose instantaneous value u = U
m
sin
ω
t is applied to a
capacitive load C [F] is expressed by the equation below.
i
=
U
m
X
C
sin
W
t +
sin
W
t +
P
2
=
I
m
P
2
Expressed using rms values, the equation is I = U/X
C
. X
C
is called capacitive reactance
and is defined as X
C
= 1/
ω
C. The unit of capacitive reactance is
Ω
.
When the polarity of the voltage changes, the largest charging current with the same
polarity as the voltage flows through the capacitor. When the voltage decreases,
discharge current with the opposite polarity of the voltage flows. Thus, the current phase
leads the voltage.
C
I
U
U
I
π
2
Appendix 3 Power Basics (Power, harmonics, and AC RLC circuits)
