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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Here are the solutions for the requested calculations: iii. Calculate the inductive reactance XL: The inductive reactance (X_L) is the opposition of an inductor to the flow of alternating current. It is given by the formula: X_L = 2 f L where f is the frequency and L is the inductance. Step 1: Identify the given values. Given frequency f = 50 Hz. Given inductance L = 0.1 H. Given = 3.14. Step 2: Substitute the values into the formula. X_L = 2 × 3.14 × 50 Hz × 0.1 H Step 3: Calculate the inductive reactance. X_L = 31.4 The unit for reactance is Ohms (). The inductive reactance is 31.4 iv. Calculate the capacitive reactance XC: The capacitive reactance (X_C) is the opposition of a capacitor to the flow of alternating current. It is given by the formula: X_C = (1)/(2 f C) where f is the frequency and C is the capacitance. Step 1: Identify the given values and convert units. Given frequency f = 50 Hz. Given capacitance C = 100 F = 100 × 10^-6 F. Given = 3.14. Step 2: Substitute the values into the formula. X_C = (1)/(2 × 3.14 × 50 Hz) × 100 × 10^-6 F Step 3: Calculate the capacitive reactance. X_C = (1)/(31400 × 10^-6) X_C = (1)/(0.0314) X_C ≈ 31.847 The capacitive reactance is 31.85 (rounded to two decimal places). v. Calculate the total impedance Z: The total impedance (Z) in a series RC circuit (resistance and capacitive reactance) is the total opposition to current flow. It is calculated using the Pythagorean theorem for phasors: Z = sqrt(R^2 + X_C^2) where R is the resistance and X_C is the capacitive reactance. Step 1: Identify the given values. Given resistance R = 10 . Given capacitive reactance X_C = 15 . Step 2: Substitute the values into the formula. Z = sqrt((10 ) )^2 + (15 )^2 Step 3: Calculate the squares of the resistance and capacitive reactance. Z = sqrt(100 ) ^2 + 225 ^2 Step 4: Sum the squared values and take the square root. Z = sqrt(325 ) ^2 Z ≈ 18.027 The total impedance is 18.03 (rounded to two decimal places). 3 done, 2 left today. You're making progress.