Identify the parallel combination.

Here are the solutions to the capacitor problems: b) (i) Calculate the effective capacitance of the arrangement. Step 1: Identify the parallel combination. The 3 µF and 1 µF capacitors are connected in parallel. The equivalent capacitance for parallel capacitors (C_p) is the sum of their individual capacitances. C_p = C_1 + C_2 C_p = 3 µF + 1 µF C_p = 4 µF Step 2: Identify the series combination. The 4 µF capacitor is in series with the equivalent parallel capacitance (C_p = 4 µF). The effective capacitance for series capacitors (C_eff) is given by: (1)/(C_eff) = (1)/(C_a) + (1)/(C_b) (1)/(C_eff) = (1)/(4 µF) + (1)/(4 µF) (1)/(C_eff) = (2)/(4 µF) (1)/(C_eff) = (1)/(2 µF) C_eff = 2 µF b) (ii) Calculate the charge on the 3 µF capacitor. Step 1: Calculate the total charge stored in the circuit. The total charge (Q_total) is stored by the effective capacitance (C_eff) at the total voltage (V_total). Q_total = C_eff × V_total Q_total = 2 µF × 12 V Q_total = 24 µC Step 2: Determine the charge and voltage for the series components. In a series circuit, the charge on each component is the same as the total charge. So, the charge on the 4 µF capacitor is 24 µC, and the charge on the parallel combination (C_p = 4 µF) is also 24 µC. Step 3: Calculate the voltage across the parallel combination. The voltage across the parallel combination (V_p) is: V_p = (Q_p)/(C_p) V_p = 24 µC4 µF V_p = 6 V Step 4: Calculate the charge on the 3 µF capacitor. Since the 3 µF capacitor is part of the parallel combination, the voltage across it is V_p = 6 V. Q_3 F = C_3 F × V_p Q_3 F = 3 µF × 6 V Q_3 F = 18 µC c) Find the separation distance between two plates if the capacitance between them is 8.0 × 10^-12 F and the area enclosed is 2.0 cm^2 (take _o = 8.85 × 10^-12). Step 1: State the formula for capacitance of a parallel plate capacitor. C = (_o A)/(d) Where C is capacitance, _o is the permittivity of free space, A is the area of the plates, and d is the separation distance. Step 2: Convert the given area to square meters. A = 2.0 cm^2 = 2.0 × (10^-2 m)^2 = 2.0 × 10^-4 m^2 Step 3: Rearrange the formula to solve for d. d = (_o A)/(C) Step 4: Substitute the given values and calculate d. d = (8.85 × 10^-12 F/m) × (2.0 × 10^-4 m^2)8.0 × 10^-12 F d = 17.7 × 10^-168.0 × 10^-12 m d = 2.2125 × 10^-4 m Rounding to three significant figures: d = 2.21 × 10^-4 m Last one today — make it count tomorrow, or type /upgrade for unlimited.