KCL : ΣI = 0 KVL: ΣV = 0 Superposition theorem: $I_L = I’_L + I”_L$ No specific formulae in Thevenin’s theorem
$$ I_2 = {R_1}/{(R_1 + R_2)} I $$ OR $$ I_1 = {R_2}/{(R_1 + R_2)} I $$ Delta to Star Conversion: E.g. $R_1 = {\text"Product of adjacent resistors in delta"}/{\text"Sum of all the resistors in delta"}$ $R_1 = {R_{12} R_{31}}/{R_{12} + R_{23} + R_{31}}$ Star to Delta Conversion: $R = R_1 R_2 + R_2 R_3 + R_1 R_3$ E.g. $R_{12} = {R}/{R_3}$ Any resistance in equivalent delta = ${\text"Total resistance R in star"}/{\text"Opposite resistance in star"}$
(1) Balanced star load: Line voltage = √3 phase voltage Line current = phase current Power Relations: Apparant Power: S = √3 $V_L I_L$ VA or kVA Active Power: P = √3 $V_L I_L$ cosϕ watt Reactive Power: Q = √3 $V_L I_L$ sinϕ kVAR (2) Balanced delta load: Line voltage = phase voltage Line current = √3 Phase current Power formulae are same as that of star load
(1) Reactance: Inductive Reactance ($X_L$) = ωL = 2πfL Capacitive Reactance ($X_C$) = 1/{ωC} (2) Impedance (Z): Z = R + jX Z = |Z|∠ϕ Magnitude, |Z| = $√{R^2 + X^2}$ Phase angle, ϕ= $tan^{-1}[X/R]$ (3) Purely resistive AC Circuit: $ v=V_m sinωt $ $ V_m = peak voltage $ $ i = I_m sinωt $ $ I_m = peak current $ $ i = I_m ∠0° $ Avg. Power, $P_{av} = V_{rms} I_{rms} $ watt Z = R i.e. Z = R∠0° (4) Purely inductive AC Circuit: $ v=V_m sinωt $ $ i = I_m sin(ωt – π/2) $ ...
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$$ v(t) = V_m sin(2πf_0 t) $$ $$ i(t) = I_m sin(2πf_0 t) $$ $$ I_{rms} = 0.707 I_m = I_m/√2 $$ $$ I_{av}= 0.637 I_m $$ $$ V_{av}= 0.637 V_m $$ Form Factor: $ K_f = I_{rms}/I_{av} $ $ K_f = 1.11$ for sinusoidal ac quantities Crest Factor: $ K_p = I_m / I_{rms} $ $ K_p = 1.414$ for sinusoidal ac quantities
(1) Coulomb’s inverse square law: $$ F = {q_1 q_2}/{4π ε_0 ε_r r^2} $$ $ε_0 = 8.854 x 10^{-12} =$ F/m ${1}/{4π ε_0}$ = 9 x $10^9$ (2) Electric flux: ψ Eletric flux density: $D = ψ/A$ C/$m^2$ Field intensity: F = E x Q $ D = ε_0 ε_r E $ Relative Permitivity ($ε_r$): Absolute permitivity, $ε = ε_r ε_0$ F/m (3) Capacitance, C = Q/V $ C = {ε_0 ε_r A}/{d} $ farad d = distance between capacitor plates (4) Capacitors in Series: $$ 1/C_{eq} = 1/C_1 + 1/C_2 + … + 1/C_n $$ (5) Capacitors in parallel: ...
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(1) Induced voltage: $$ E = 4.44 f ϕ_m N $$ (2) Ratios: Voltage ratio: $ V_1/V_2 $ Transformation ratio: $K = V_2/V_1 = E_2/E_1 = N_2 / N_1 $ Turns ratio: $N_1/N_2$ $$ I_1/I_2 = V_2 / V_1 $$ (3) Rating of Transformer: $$ I_1 = {kVA 10^3}/{V_1} $$ (4) Copper Loss: $$ P_{cu} = I_1_^2 R_1 + I_2_^2 R_2 $$ $$ P_{cu(HL)} = {(1/2)}^2 P_{cu(FL)} $$ (5) Iron Loss: $P_i$ = Hysteresis Loss + eddy current loss Hysteresis loss: $P_H = K_H B_m_^{1.67} f V$ Eddy current loss = $ I^2 $ x r (6) Resistance transfered to ...
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(1) Induced EMF: $ e = – N dϕ/dt $ volts e = B x l x v volts (2) Inductance: $ L = {N ϕ}/{I} $ Henry $$ e = -L [{dI}/{dt}] $$ (3) Coefficient of self-inductance: $ L = {N^2 μ_0 μ_r a}/{l} $ N = Number of turns l = length of magnetic circuit a = Cross sectional area of magnetic circuit (4) Mutual Inductance: $ e_2 = -M {dI_1}/{dt} $ $M = {N_2 K ϕ_2}/{I_1}$ $ M = {N_1 N_2 μ_0 μ_r1 a_1 }/{l_1} $ (5) Coefficient of Coupling (K): $M = K √{L_1 L_2}$ $K ...
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(1) Coulumb’s Law: $$ F = K {m_1 m_2}/{d^2} $$ (2) Magnetic Flux Density: $ B = ϕ / A $ 1 Weber = $10^8$ lines of force (3) Magnetic Field Strength (H): $$ H = {\text"Ampere Turns"}/{\text"length in metre"} $$ Multiple conductors: $H = {N I}/{2πr} $ A/m Solenoid: $H = {N I}/{d}$ AT/m (4) Permeability: Absolute Permeability (μ) = B/H henry per metre Permeability of free space ($μ_0$) = B/H in vaccum or air $μ_0$ is 4π x $10^{-7}$ H/m Relative permeability ($μ_r$) = $B/{B_0}$ H is same $ μ = μ_0 μ_r $ H/m $B = μ_0 ...
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(1) Resistance (R) & Resistivity (ρ): R = 1/G where, G = Conductance $$R = ρ l/a$$ l = length a = area of cross section Extra: Volume = a x l (2) Resistances in Series: $$R_T = R_1 + R_2 + R_3 + …$$ where, $R_T$ = Effective Resistance (3) Resistances in parallel: $$ 1/R_T = 1/R_1 + 1/R_2 + 1/R_3 + ….. $$ Note : $ R_T = {R_1 R_2}/{R_1 + R_2} $ (4) Ohm’s Law: $$V = I R$$ where, V = voltage I = current R = resistance (5) Resistance Temperature Coefficient (R.T.C.): RTC ...
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