INDUCTOR Rules
CAPACITOR Rules
ELI the ICEman
ELI the ICE-man
(E before I for L)
(I before E for C)
VL
VC
iL
90º
π
π/2
0
-π/2
iC
3π/2
2π
-π/2
π/2
0
t0 initial
conditions
t0 initial conditions
Using t0 for phase: v = 5 sin(wt) i = 2 sin(wt + 90º)
The rising current crosses the x-axis 90º before the voltage
To represent the current phase in the time domain show a +90º.
If iC crossed after t0 the current phase would be negative
Switch closes at t=0
time
0+
Current
0
imax
Switch closes at t=0
VL
Vmax
0
time
0+
Vector diagram
Inductance contributes positive volts-amps-reactance (VAR)
in the power triangle seen below. The absolute value of cos Ø
is the power factor.
Ø
Q
P
Watts
I-V Phasor diagram are different from the power triangle.
0º is at 3 o’clock. CCW rotation represents increasing time.
Ø
S
Ø
Ø
VAR
VA
P
Q
I-V Phasor diagram are different from the power triangle.
0º is at 3 o’clock. CCW rotation represents increasing time.
I
V
I
Capacitance contributes negative volts-amps-reactance (VAR)
in the power triangle seen below. The absolute value of cos Ø
is the power factor.
Watts
S
VAR
Ø
VC
0
Vmax
Use -90 for capacitors or -j
Use +90 for inductors or +j
VA
Current
imax
0
Vector diagram
R
Xc
Z
XL
R
2π
90º
Using t0 for phase: i = 2 sin(wt) then v = 5 sin(wt + 90º)
The rising voltage crosses the x-axis 90º before the current.
To represent the voltage phase in the time domain show a +90º.
If VL crossed after t0, the voltage phase would be negative
Z
3π/2
π
I & V are vectors with length and direction
For inductive circuits, I lags V
The above diagram shows a lagging power factor.
To line up the current with the voltage add Ø
V
Ø
For capacitive circuits, I leads V
The above diagram shows a leading power factor.
To line up the current with the voltage subtract Ø
XL=2π.f.L formula to calculate the inductive reactance
XC=1/(2π.f.C) formula to calculate the capacitive reactance
Wye Circuits
S = P ± jQ
S = V·I
cos-1(P/S) = Ø
Vline=
.
3 Vphase
Iline=Iphase
Delta Circuits
Vline=Vphase
Iline= 3 .Iphase
Q = S·sin(Ø)
P = S·cos(Ø)
FP = cos(Ø) = P/S