  Circuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 201 p.)  11. Basic symbols and formulas of electrical engineering  (introduction...) 11.1. General direct current engineering 11.2. Magnetic field 11.3. Law of induction 11.4. Electric field 11.5. Alternating current engineering 11.6. Calculation of power

(introduction...)

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 = gyro-frequency in or Hz f = frequency in or Hz C = capacity in F r = resistivity in c = unit conductance in A = conductor cross-section in mm2 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 RK = resistance at initial temperature RW = resistance at final temperature µ = temperature coefficient in p = 3,14

influence of the temperature on the resistance of the conductor 11.1. General direct current engineering

 Ohm’s Law power P = U2 · I [W] P = I2 · R [W] [W] work W = U · I · t [V · A · s = Ws] W = P · t [W · s = Ws] diameter of a conductor [mm2] resistance of a conductor [W] [W] influence of temperature on the resistance of the conductor RW = RK [1 + µ(J2 - J1)]

Connection of resistances and power sources

· series connection Figure Figure

RG = R1 + R2 + R3 (total resistance)

U = U1 + U2 + U3.....

EG = E1 + E2 + E3 condition: Ri1 = Ri2 = Ri3

U = I · Ra

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

 RE = equivalent resistance IG = total current intensity Condition: Equal power sources are connected in parallel. E = E1 = E2 = E3 for 2 resistances connected for n equal resistances IG = I1 + I2 + I3

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.

IG - I1 - I2 - I3 = 0 Figure

11.2. Magnetic field

 flux: magnetic flux: magnetic resistance: 1 = magnetically effective length in m A = flux passage area in m2 comparative figure ur for air = 1, 000 000 4 magnetic permeability relative permeability mr - comparative figure induction constant magnetic field strength magnetic induction B = m · H = mo · mr · H 11.3. Law of induction

 induced voltage [V] self-induction - self-inductance [H] [H] - voltage of the self-induction [V]

11.4. Electric field

 electric field strength  = voltage in V = thickness of the dielectric in m charge Q = I · t [As] capacity [F] Q = quantity of electricity in AS C in F (1F = 1 AS/V) equation of dimensioning dielectric constant relative dielectric constant er: matter constant, relative to the vacuum absolute dielectric constant dielectric flux density D = e · E

11.5. Alternating current engineering

 frequency T = cycle duration in s gyro-frequency phase angle instantaneous value of a sinusoidal a.c. voltage instantaneous value of a sinusoidal a.c. current maximum value - of a sine-wave 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 UR = I · R [V] inductive voltage drop UL = I · XL = I · w L [V] capacitive voltage drop [V] Ohm’s law for alternating current [A]

Powers in case of single-phase 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 three-phase alternating current

 apparent power [VA] active power [W] reactive power [Var] power factor efficiency for motors and generators Pe = effective power Pi = indicated power speed calculation of three-phase motors rotating field speed  p = number of pole pairs slip [%] n = rotor speed

11.6. Calculation of power

calculation of power losses

PV = power loss in per cent

direct current [%]

single-phase alternating current [%]

three-phase alternating current [%] [V]; [V] [V]; [V] [V]; [V]

Determination of a conductor cross-section

- Calculation of the rated current from current, voltage and power factor.

- Division by all suitable current-carrying capacity factors of the Tables 9 to 12.

- Determination of the conductor cross-section according to the given current-carrying capacity factors after the calculated fictive current.

- Calculation of the conductor cross-sections according to the given power and voltage loss.

- Comparison of the cross-sections found out under the third and fourth point. The greatest is chosen as the cross-section to be installed.

Conversion of the measuring units of work and power

Work

 J erg kpm kWh PSh kcal 1 1 107 0.102 0.278 · 10-6 0.378 · 10-6 0.239 · 10-3 107 1 0.102 · 10-7 0.278 · 10-13 0.378 · 10-13 0.239 · 10-10 9.81 9.81 · 107 1 2.72 · 10-6 3.70 · 10-6 2.34 · 10-3 3.60 · 106 3.60 · 1013 3.67 · 105 1 1.36 860 2.65 · 106 2.65 · 1013 2.70 · 105 0.7355 1 632 4187 4.19 · 1010 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 0.86 103 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