This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Q1: R-L Series Circuit Given: R = 30\ , L = 0.127\ H, V = 220\ V, f = 50\ Hz. a) Inductive reactance X_L Step 1: Calculate the inductive reactance using the formula X_L = 2 f L. X_L = 2 (50\ Hz) (0.127\ H) X_L = 39.898\ X_L = 39.90\ b) Total impedance Z Step 2: Calculate the total impedance using the formula Z = sqrt(R^2 + X_L^2). Z = sqrt((30\ )^2 + (39.898\ )^2) Z = sqrt(900\ ^2 + 1591.85\ ^2) Z = sqrt(2491.85\ ^2) Z = 49.918\ Z = 49.92\ c) Current I Step 3: Calculate the current using Ohm's law for AC circuits, I = (V)/(Z). I = 220\ V49.918\ I = 4.407\ A I = 4.41\ A d) Power factor Step 4: Calculate the power factor using the formula = (R)/(Z). = (30\ )/(49.918\ ) = 0.6009 Power factor = 0.601 Q2: R-C Series Circuit Given: R = 100\ , C = 25\ F = 25 × 10^-6\ F, V = 240\ V, f = 60\ Hz. a) Capacitive reactance X_C Step 1: Calculate the capacitive reactance using the formula X_C = (1)/(2 f C). X_C = (1)/(2 (60\ Hz)) (25 × 10^-6\ F) X_C = (1)/(0.00942477) X_C = 106.103\ X_C = 106.10\ b) Impedance Z Step 2: Calculate the impedance using the formula Z = sqrt(R^2 + X_C^2). Z = sqrt((100\ )^2 + (106.103\ )^2) Z = sqrt(10000\ ^2 + 11258.04\ ^2) Z = sqrt(21258.04\ ^2) Z = 145.801\ Z = 145.80\ c) Current I Step 3: Calculate the current using Ohm's law for AC circuits, I = (V)/(Z). I = 240\ V145.801\ I = 1.646\ A I = 1.65\ A d) Phase angle . State if leading or lagging. Step 4: Calculate the phase angle using = (-X_C)/(R). = (-106.103\ )/(100\ ) = -1.06103 = (-1.06103) = -46.69^ In an R-C series circuit, the current leads the voltage. = -46.69^, Current leads voltage Q3: R-L-C Series Circuit Given: R = 50\ , L = 0.2\ H, C = 50\ F = 50 × 10^-6\ F, V = 230\ V, f = 50\ Hz. a) X_L and X_C Step 1: Calculate the inductive reactance X_L = 2 f L. X_L = 2 (50\ Hz) (0.2\ H) X_L = 62.832\ Step 2: Calculate the capacitive reactance X_C = (1)/(2 f C). X_C = (1)/(2 (50\ Hz)) (50 × 10^-6\ F) X_C = (1)/(0.01570796) X_C = 63.662\ X_L = 62.83\ , X_C = 63.66\ b) Net reactance Step 3: Calculate the net reactance X_net = X_L - X_C. X_net = 62.832\ - 63.662\ X_net = -0.83\ X_net = -0.83\ c) Impedance Z Step 4: Calculate the impedance using the formula Z = sqrt(R^2 + (X_L - X_C)^2). Z = sqrt((50\ )^2 + (-0.83\ )^2) Z = sqrt(2500\ ^2 + 0.6889\ ^2) Z = sqrt(2500.6889\ ^2) Z = 50.0069\ Z = 50.01\ d) Current I Step 5: Calculate the current using Ohm's law for AC circuits, I = (V)/(Z). I = 230\ V50.0069\ I = 4.599\ A I = 4.60\ A e) Real power P Step 6: Calculate the real power using the formula P = I^2 R. P = (4.599\ A)^2 (50\ ) P = (21.1508\ A^2) (50\ ) P = 1057.54\ W P = 1057.54\ W Send me the next one 📸