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's the solution for Task 2: Task 2, Part i: i. Simplify the formula for the current I to its most basic form. Step 1: Write down the given formula and values. The formula is I = k × S^m / S^n. Given constants are k=5, m=3, n=2. Step 2: Substitute the given values into the formula. I = 5 × S^3 / S^2 Step 3: Apply the law of indices (a^x)/(a^y) = a^x-y. I = 5 × S^(3-2) I = 5 × S^1 I = 5S The simplified formula for current I is I = 5S. Task 2, Part ii: ii. Draw a circuit diagram showing how to connect the four batteries in parallel to increase capacity while maintaining 12V. To connect four batteries in parallel, all positive terminals are connected together, and all negative terminals are connected together. This maintains the voltage (e.g., 12V if each battery is 12V) while increasing the total current capacity (Ah). A circuit diagram would show: • Four battery symbols arranged side-by-side. • A common line connecting all the positive terminals of the batteries. • Another common line connecting all the negative terminals of the batteries. • The output terminals would be taken from these two common lines. Task 2, Part iii: iii. Calculate the inductive reactance XL. Step 1: Write down the formula for inductive reactance and given values. The formula for inductive reactance is X_L = 2 f L. Given values are f = 50Hz, L = 0.1H, and = 3.14. Step 2: Substitute the values into the formula. X_L = 2 × 3.14 × 50Hz × 0.1H Step 3: Calculate the result. X_L = 314 × 0.1 \, X_L = 31.4 \, The inductive reactance X_L is 31.4 . Task 2, Part iv: iv. Calculate the capacitive reactance XC. Step 1: Write down the formula for capacitive reactance and given values. The formula for capacitive reactance is X_C = (1)/(2 f C). Given values are f = 50Hz, C = 100 F, and = 3.14. Convert capacitance to Farads: C = 100 F = 100 × 10^-6 F = 1 × 10^-4 F. Step 2: Substitute the values into the formula. X_C = (1)/(2 × 3.14 × 50Hz × (1 × 10^-4) F) Step 3: Calculate the result. X_C = (1)/(314 × 10^-4) \, X_C = (1)/(0.0314) \, X_C ≈ 31.847 \, The capacitive reactance X_C is 31.85 . Task 2, Part v: v. Calculate the total impedance Z. Step 1: Write down the formula for total impedance in a series RC circuit and given values. The formula for impedance in a series RC circuit is Z = sqrt(R^2 + X_C^2). Given values are R = 10 and X_C = 15. Step 2: Substitute the values into the formula. Z = sqrt((10)^2 + (15)^2) Step 3: Calculate the squares. Z = sqrt(100^2 + 225^2) Step 4: Sum the squared values and take the square root. Z = sqrt(325^2) Z ≈ 18.0277 \, The total impedance Z is 18.03 . That's 2 down. 3 left today — send the next one.