ELTK1200 Formula Sheet
Induced voltage
Power Factor
Capacitance
Frequency
Resistors in series
Angular velocity
Resistors in parallel
Peak, Peak to Peak, RMS
Capacitors in series
Capacitors in parallel
Inductors in series
Real Inductor
Inductors in parallel
Q-Factor
1
Pure resistor
Instantaneous equations
RMS
Instantaneous waveforms
Phasor Diagram
Phase Relationship:
I and VS are “in phase”.
2
Pure inductor
Instantaneous equations
I as reference.
RMS
VS as reference (See Note).
Instantaneous waveforms
Phasor Diagram
I as reference (starts at 0).
Phase Relationship:
I lags VS by 90°.
Note: The instantaneous equations depend upon which waveform is taken as a reference.
Phasor diagrams use current I as a reference, but sometimes problems give VS as
reference (
) and you must calculate I.
For the rest of this formula sheet, current I will be the reference.
3
Series RL circuit
Instantaneous equations
Instantaneous waveforms
RMS
Impedance Triangle
Phasor Diagram
Power Triangle
Phase Relationship: I lags VS by 2 (angle between 0° and 90°).
4
Pure capacitor
Instantaneous equations
RMS
Phasor Diagram
Instantaneous waveforms
Phase Relationship:
I leads VS by 90°.
5
Series RC circuit
Instantaneous equations
Instantaneous waveforms
RMS
Impedance Triangle
Phasor Diagram
Power Triangle
Phase Relationship: I leads VS by 2 (angle between 0° and 90°).
6
Series RLC circuit
Instantaneous equations and
waveforms depend on
whether the angle is lagging
(See Series RL circuit) or
leading (See Series RC circuit).
NOTE: If XL > XC (VL > VC, QL > QC), circuit is
inductive, ˆ lagging phase angle. If XL < XC (VL < VC, QL
< QC), circuit is capacitive, ˆ leading phase angle. If XL
= XC (VL = VC, QL = QC), circuit is resistive, ˆ in phase,
resonant frequency.
Impedance Triangle
Phasor Diagram
RMS
Power Triangle
Phase Relationship: I leads/lags VS by 2 (between 0° and 90°). Lagging phase angle
shown. See NOTE.
7
Resonant frequency
Three phase
Wye (Y)
Delta ())
Power
General Transformer equation
Relationship between I and VS for all Series Circuits.
L
RL
R
RC
C
Inductive
Transformation ratio
Resistive
Capacitive
1
Transformer capacity
I lags VS by 90°.
I lags VS by 2. 2
I and VS are in phase.
I leads VS by 2. 2
I leads VS by 90°.
RLC I leads/lags VS by 2. 1
1
2
Depends on values of L, C and f.
between 0° and 90°.
ELI the ICEman drinks RIE.
ELI drinks RIE and ICE.
Transformer losses and efficiency
8
ELI = I lags VS by 90° for L circuits.
RIE = I and VS are in phase for R circuits.
ICE = I leads VS by 90° for C circuits.
rev 5