Theory and industrial applications of electricity Basic electrical phenomena Laws of electrotechnics & applications DC circuits & Kirccoffs laws Single phase & three phase AC circuits AC and DC motors

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matterelementary charge: e- = - 1.60210-19 C positive charged body has lost electrons positive charge attracted by negative and repelled by positive charge negative charged body has gained electronsnegative charge attracted by positive and repelled by negative charge

FF

[E] = V/m

[D] = C/m2

0 = 1/(4910 9) F/m

Coulombs LawF12 = F21= q1q2/(40r2)F12 = q1E2 >> E2 = q2/(40r2)F21 = q2E1 >> E1 = q1/(40r2)

q1 = 1 pCq2 = 2 pCF12 = F21 = ? F12 = F21 = q1q2/(40r2) = 210-24/(4010-6) = 210-8 N spheres, 2r = 100 m = 1300 kg/m3 (PVC)F12/Fg = ?Fg = Vg = (4r3/3)gFg = 13004(510-5)39.81/3 Fg = 6.810-9 N F12/Fg = 210-8/6.810-9 = 3

The voltage between two points of a path is expressed as the line integral of the electric field. UAB = VA - VB

When a dielectric is placed in an external electric field its molecules gain electric dipole moment and the dielectric is said to be polarized

Polarization density: P = dp/dV [P] = C/m2

Polarization law: P = 0eEe electric susceptibility

A capacitor consists of two conductors separated by an electrical insulator (dielectric)

C = 0rl/ln(R2/R1)WC = (1/2)qU = (1/2)CU2 = (1/2)q2/C [J] wC = WC/V = (1/2)0rE2 [J/m3]C = 40r/(1/R1-1/R2)C = 0r A/d

V1 = V2i = dq/dt [i] = AThe electric current is defined to be the rate of which charges pass through a cross-sectional area of the conductor

n = number of charge carriers per unit of volumeq = charge of each carriervd = drift speed (speed of charge carriers)q = qnV = qnAvdti = q/t = qnAvd vdt

In a material the current density J is linearly dependent on the external electric field E

(J = i/A) uAB = ilAB/A = iRAB

Conductor resistance : RAB = lAB/A R = l/A [R] = Macroscopic version of the Ohms lawu = Ri Conductivity of some conductive materials:Silver (Ag): = 6.3107 S/m, = 0.0038 1/CCopper (Cu): = 5.8107 S/m, = 0.0039 1/CAluminium (Al): = 3.5107 S/m, = 0.0039 1/CIron (Fe): = 1.0107 S/m, = 0.0045 1/C

DC = Direct Current unidirectional flow of electric charges DC supplies E (EMF = electromotive force) Resistors R (resistance)

Kirchhoffs current law

Kirchhoffs voltage law

Kirchhoffs voltage law

E1 + E2 - E3 = R1I1 + R2I2 - R3I3 - R4I4

travel direction

ApplicationKirchhoffs current low:I1 + I4 = I6I2 + I5 = I1I3 + I6 = I2

Kirchhoffs voltage law:R1I1 + R5I5 R4I4 = E5R2I2 + R3I3 R5I5 = -E5R6I6 + R4I4 R3I3 = E6

ApplicationR1 = 2R2 = 2R3 = 4E1 = 20 VE2 = 10 VUR3 = ?I1 = I2 + I3E1 = R1I1 + R3I3E2 = R2I2 - R3I3

The rate of energy loss (heat) generated by a constant current in any part of an electrical circuit is proportional to the resistance and to the square of the currentP =RI2P =UIP = U2/R[P] = W

P =UIU = EP = EI