customary, definitions and formulae

Reading time:

direct current


formula: intensity


formula: resistance

alternating current

power factor or cos Ø

Intensity and an alternating current voltage will rarely be in phase. The cosinus for the angle formed by the two intensity voltage vectors is called the power factor.

When a self-inductor is incorporated into a circuit, it steps the intensity back from the voltage; when a capacitance is incorporated, it has the opposite effect.

The active power is decreased in both cases (figure 45).

In the case of an industrial sinusoidal current (normal case) :

  • Ia = I cos Ø is the active current;
  • Ir = I sin Ø is the reactive current.
circuit comprising self-inductionSecured image
Figure 45. Case of a circuit comprising a self-induction

apparent, active, reactive power

I is the intensity read off an ampere meter, U the main voltage between phases, for a three phase supply.

u is the mains voltage between phase and neutral, for a single phase supply, power is detailed in table 75.

Apparent - activ - reactive powerSecured image
Table 75. Apparent, active, reactive power

The apparent power is expressed in volt-amperes (VA).

Active power is expressed in Watts (W).

The reactive power is expressed in reactive volt-amperes (VAr).

A poor cos Ø is detrimental to both the energy user and to the distributor. It requires large conduit sections and higher apparent power levels for alternators and transformers.

circuit impedance

Circuit impedance is the resultant of the ohmic resistance and the circuit’s reactance.

formula:  Circuit impedance

R = resistance,

X = reactance (inductive, capacitive).

Amount of heat given off by a circuit having a resistance R and crossed by a current I for one second.

formula: Amount of heat given off by a circuit

star assembly – delta assembly

Resistances and motor windings can be connected in star or delta configuration. Figure 46 recaps the properties of both these configurations.

Star and delta connectionsSecured image
Figure 46. Star and delta connections