Question Detail
Question
In a parallel-plate capacitor, the distance d between the plates is 3cm, the area of each plate is 15cm², and the voltage across them is 5V. Calculate the capacitance. Take permittivity of free space to be ε₀ = 8.854 × 10⁻¹² C²/Nm².
Correct Answer
Option C is the correct answer.
Detailed Explanation
The capacitance (C) of a parallel-plate capacitor is given by the formula C = ε₀ * A / d, where:ε₀ = permittivity of free space = 8.854 × 10⁻¹² F/mA = area of the plates = 15 cm² = 15 × 10⁻⁴ m²d = distance between the plates = 3 cm = 3 × 10⁻² mC = (8.854 × 10⁻¹² F/m) * (15 × 10⁻⁴ m²) / (3 × 10⁻² m)C = (8.854 × 15 / 3) × 10⁻¹² × 10⁻⁴ / 10⁻² FC = (8.854 × 5) × 10⁻¹⁴ FC = 44.27 × 10⁻¹⁴ F = 4.427 × 10⁻¹³ F.Rounding to two decimal places, this is 4.43 × 10⁻¹³ F.
Hint
Remember the formula for capacitance of a parallel-plate capacitor: C = ε₀A/d. Pay close attention to unit conversions from cm to m.