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
Phase Relationship: I as reference (starts at 0). 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 RMS 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 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 I lags VS by 90°. Inductive 2 RL I lags VS by 2. Transformation ratio Resistive R I and VS are in phase. RC I leads V by 2. 2 Capacitive S C I leads VS by 90°. 1 1 RLC I leads/lags VS by 2. Transformer capacity 1 Depends on values of L, C and f. 2 between 0° and 90°.
ELI the ICEman drinks RIE. ELI drinks RIE and ICE.
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. Transformer losses and efficiency
8 rev 5