Circuits, Formulas and Tables Electrical Engineering  Basic vocational knowledge (Institut für Berufliche Entwicklung, 201 p.) 
11. Basic symbols and formulas of electrical engineering 

The following is valid:
I 
= current intensity in A  
E 
= empressed voltage in V  
U 
= voltage, terminal voltage in V  
R 
= resistance in w  
L 
= inductivity in H 
_{}  
w 
= gyrofrequency in _{} or Hz  
f 
= frequency in _{} or Hz 

C 
= capacity in F 
_{}  
r 
= resistivity in _{}  
c 
= unit conductance in _{} 

A 
= conductor crosssection in mm^{2}  
d 
= diameter in mm  
P 
= power in W (active power)  
Q 
= reactive power in Var  
S 
= apparent power in VA  
W 
= work in Wh or Ws  
cos j 
= power factor  
h 
= efficiency  

= flux in A  
B 
= magnetic induction in T or _{}or_{}  
H 
= magnetic field strength in _{}  
E 
= electric field strength in _{}  
f 
= magnetic flux in Wb or Vs  
F 
= force in N 
_{}  
v 
= velocity in _{}  
w 
= number of turns  
t 
= time in s or h  
J K 
= initial temperature  
J W 
= final temperature  
R_{K} 
= resistance at initial temperature  
R_{W} 
= resistance at final temperature  
µ 
= temperature coefficient in _{}  
p 
= 3,14 
influence of the temperature on the resistance of the conductor _{}
Ohm’s Law 
_{}  
power 
P = U_{2} · I 
[W] 

P = I^{2} · R 
[W] 

_{} 
[W] 
work 
W = U · I · t 
[V · A · s = Ws] 

W = P · t 
[W · s = Ws] 
diameter of a conductor 
_{} 
[mm^{2}] 
resistance of a conductor 
_{} 
[W] 

_{} 
[W] 
influence of temperature on the resistance of the conductor 
R_{W} = R_{K} 
[1 + µ(J_{2}  J_{1})] 
Connection of resistances and power sources
· series connection
Figure
Figure
R_{G} = R_{1} + R_{2} + R_{3} (total resistance)
U = U_{1} + U_{2} + U_{3}.....
E_{G} = E_{1} + E_{2} + E_{3}
_{} 
condition: R_{i1} = R_{i2} = R_{i3} 
U = I · R_{a}
2. Kirchhoff’s Law
The sum of all voltages around a closed path in an electrical system is zero.
_{}
The sum of the impressed voltage is equal to the sum of the voltage drops.
· parallel connection
Figure
Figure
R_{E} = equivalent resistance  
I_{G} = total current intensity  
_{} 
Condition: 

Equal power sources are connected in parallel. 

E = E_{1} = E_{2} = E_{3} 
for 2 resistances connected 
_{} 
for n equal resistances 
_{} 

I_{G} = I_{1} + I_{2} + I_{3} 
1. Kirchhoff’s Law
At each junction the sum of the currents flowing toward the junction is equal to the sum of the currents flowing away from the junction.
I_{G}  I_{1}  I_{2}  I_{3} = 0
Figure
flux: 
_{} 
magnetic flux: 
_{} 
magnetic resistance: 
_{} 
1 = magnetically effective length in m  
A = flux passage area in m^{2}  
_{}  
comparative figure u_{r} for air = 1, 000 000 4 

magnetic permeability 
_{} 
relative permeability 
m_{r}  comparative figure 
induction constant 
_{} 
magnetic field strength 
_{} 
magnetic induction 
B = m · H = m_{o} · m_{r} · H 

_{} 
induced voltage 
_{} 
[V]  
selfinduction 
  

 selfinductance 
_{} 
[H] 
 
_{} 
[H] 

 voltage of the selfinduction 
_{} 
[V] 
electric field strength 
_{} 
_{}  

= voltage in V 
 

= thickness of the dielectric in m  

charge 
Q = I · t 
[A_{s}]  
capacity 
_{} 
[F]  

Q = quantity of electricity in A_{S}  


C in F (1F = 1 A_{S}/V)   
equation of dimensioning 
_{}   
dielectric constant 
_{}   
relative dielectric constant 
e_{r}: matter constant, relative to the vacuum  

absolute dielectric constant 
_{}   
dielectric flux density 
D = e · E  
frequency 
_{}  

T = cycle duration in s  
gyrofrequency 
_{}  
phase angle 
_{}  
instantaneous value of a sinusoidal a.c. voltage 
_{}  
instantaneous value of a sinusoidal a.c. current 
_{}  
maximum value 
 

 of a sinewave voltage 
_{} 

U = virtual value 


 of a sine current 
_{} 

I = virtual value 


inductive resistance 
_{} 
(inductive reactance) 
L in H  
capacitive resistance 
_{}  
(capacitive reactance) 
C = capacity in F 
Series connection
impedance 
_{} 
[W] 
ohmic drop in voltage 
U_{R} = I · R 
[V] 
inductive voltage drop 
U_{L} = I · X_{L} = I · w L 
[V] 
capacitive voltage drop 
_{} 
[V] 
Ohm’s law for alternating current 
_{} 
[A] 
Powers in case of singlephase alternating current
apparent power 
S = U · I 
[VA] 
active power 
P = U · I · cos z 
[W] 
reactive power 
Q = U · I · sin z 
[Var] 
power factor 
_{}  
Powers in case of threephase alternating current
apparent power 
_{} 
[VA]  
active power 
_{} 
[W]  
reactive power 
_{} 
[Var]  
power factor 
_{}   
efficiency for motors and generators 
_{}   

P_{e} = effective power   

P_{i} = indicated power   
speed calculation of threephase motors rotating field speed 
_{} 
_{}  

p = number of pole pairs   
slip 
_{} 
[%]  

n = rotor speed 

calculation of power losses
P_{V} = power loss in per cent
direct current
_{} 
[%] 
singlephase alternating current
_{} 
[%] 
threephase alternating current
_{} 
[%]   
_{} 
[V]; 
_{} 
[V] 
_{} 
[V]; 
_{} 
[V] 
_{} 
[V]; 
_{} 
[V] 
Determination of a conductor crosssection
 Calculation of the rated current from current, voltage and power factor. Division by all suitable currentcarrying capacity factors of the Tables 9 to 12.
 Determination of the conductor crosssection according to the given currentcarrying capacity factors after the calculated fictive current.
 Calculation of the conductor crosssections according to the given power and voltage loss.
 Comparison of the crosssections found out under the third and fourth point. The greatest is chosen as the crosssection to be installed.
Conversion of the measuring units of work and power
Work
J 
erg 
kpm 
kWh 
PSh 
kcal 
1 1 
10^{7} 
0.102 
0.278 · 10^{6} 
0.378 · 10^{6} 
0.239 · 10^{3} 
10^{7} 
1 
0.102 · 10^{7} 
0.278 · 10^{13} 
0.378 · 10^{13} 
0.239 · 10^{10} 
9.81 
9.81 · 10^{7} 
1 
2.72 · 10^{6} 
3.70 · 10^{6} 
2.34 · 10^{3} 
3.60 · 10^{6} 
3.60 · 10^{13} 
3.67 · 10^{5} 
1 
1.36 
860 
2.65 · 10^{6} 
2.65 · 10^{13} 
2.70 · 10^{5} 
0.7355 
1 
632 
4187 
4.19 · 10^{10} 
427 
1.16 · 10^{3} 
1.58 · 10^{3} 
1 
Power
W 
kW 
kpm s^{1} 
PS 
kcal s^{1} 
kcal h^{1} 
1 
10^{3} 
0.102 
1.36 · 10^{3} 
2.39 · 10^{4} 
0.86 
10^{3} 
1 
102 
1.36 
0.239 
860 
9.81 
9.81 · 10^{3} 
1 
0.0133 
2.34 · 10^{3} 
8.43 
735.5 
0.7355 
75 
1 
0.1757 
632 
4187 
4.19 
427 
5.69 
1 
3600 
1.16 
1.16 · 10^{3} 
0.119 
1.58 · 10^{3} 
2.78 · 10^{4} 
1 