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Formulas of electrotechnic and electronic Ohm’s Law The current intensity (I) is proportional to voltage (U) and inversely proportional to resistance (R) d p ? n or d2 ? 0,7854 ? n 4 Diameter for single wires cross-section 2 q = qffiffiffiffiffiffiffiffiffi q4 p D = pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 1; 2732 or Diameter for bunched wires D = q D d n = = = = pffi 1; 34 n d cross-section (mm2) conductor diameter (mm) single wire diameter (mm) number of wires Conductor Resistance l = or R kq RLoop = 2l kq R RLoop q k (Kappa) r (Rho) l = = = = = = Electrical direct-current resistant (Ohm) Resistance of a complete circuit cross-section (mm2 or q mm) Conductivity Specific resistance (r = k1 ) Conductor length (m) Conductivity Spec. resistance m W mm2 W mm2 m Copper 58,00 0,01724 Aluminium 33,00 0,0303 Silver 62,00 0,1613 Materials Iron 7,70 0,1299 Constantan 2,00 0,50 Serial connection Resistance: R ¼ R1 þ R2 þ R3 þ ::: þ Rn þ C11 þ C12 þ C13 þ ::: þ C1n Capacitance: 1 C Inductance: L ¼ L1 þ L2 þ L3 þ ::: þ Ln Parallel connection Resistance: R = R1 1 Capacitance: þ R12 þ R13 þ ::: R1n C ¼ C1 þ C2 þ C3 þ :::Cn L = L1 þ L1 þ L1 þ ::: L1 n 1 3 2 Equivalent resistance of 2 parallel connected resistance Inductance: R R R = R 1 þ R2 1 2 Mutual capacity (C) r 103 * coaxial cable C= (nF/km) 18 In Da d * parallel core C= r 103 (nF/km) 36 In Da d * shielded twisted pair r 103 CB = (nF/km) ðDa2 a2 Þ 36 In 2a 2 2 d Da = Ds = d = a = = T 96 = = = = U R R = UI U = I ? R current intensity (Amps – A) electrical resistance (W) electrical voltage (V) Conductance 1 = G = 1R 1S = 11W or 1 mS 1MW S (Siemens) = reziprocal value of a resistance is used as conductance 1 Siemens = 1/Ohm G = electrical conductance Capacitance Single core against earth r 103 CB = (nF/km or pF/m) 18 In Di d * Unshielded symmetrical twisted pair r 103 CB = (nF/km or pF/m) 36 In 2a d * Coaxial pair r 103 (nF/km or pF/m) CB = 18 In Di d * Shielded symmetrical twistet pair r 103 (nF/km or pF/m) CB = ðDa2 a2 Þ 36 In 2a 2 2 d * rl q 2l p q or I I R U R Cross-section for single wire round D2 p q = or D2 ? 0,7854 4 Cross-section for bunched wire ðDa þa Þ Outer diameter over insulation diameter over shield diameter of conductor distance – mid to mid of both conductors dielectric constant Di = Da = d = a = ðDa þa Þ outer diameter over single core (mm) outer diameter of multicores (mm)) conductor diameter (mm) distance between two conductors – mid to mid of both conductors Inductance of parallel cores at low frequencies L = 0,4 (In Da r + 0,25) mH/km at high frequencies L = 0,4 (In Da r + 0) mH/km Inductance of coaxial cable at high frequencies L = 0,2 (In Da r + 0) mH/km Da = distance between two conductors – mid to mid of both conductors r = radius of a conductor r = dielectric constant Impedance (Z) for coaxial cable D = d = 60 D Z = pffiffiffi ? In d (W) r diameter over insulation conductor diameter for communication cable at low frequencies Z= at R L C w high frequencies Z= = Resistance (W/km) = Inductance (mH/km) = Capacitance (nF/km) = 2pf qffiffiffiffiffiffi R = = w C (W) ? tan j 1, j 458 qffiffiffiffi L C (W) Wave length l = vf l = wave length v = propagation velocity (velocity of light: 300 000 km/s) f = frequency units of attenuation – Neper (N), decibel (dB) and Bel (B) 1 Np = 8,686 dB 1 Bel 1 dB = 0,1151 Np = 10 1 Bel = 10 dB = 1,1513 Np