What is the capacitance of a parallel plate capacitor with area 0.1 m² and separation 0.01 m filled with air (ε₀ = 8.85 × 10^-12 F/m)?
Correct Answer: 8.85 × 10^-10 F
- Step 1: Identify the formula for capacitance of a parallel plate capacitor, which is C = ε₀ * A / d.
- Step 2: Note the values given in the question: ε₀ (permittivity of free space) = 8.85 × 10^-12 F/m, area A = 0.1 m², and separation d = 0.01 m.
- Step 3: Substitute the values into the formula: C = (8.85 × 10^-12 F/m) * (0.1 m²) / (0.01 m).
- Step 4: Calculate the numerator: 8.85 × 10^-12 F/m * 0.1 m² = 8.85 × 10^-13 F·m.
- Step 5: Calculate the denominator: 0.01 m.
- Step 6: Divide the numerator by the denominator: C = (8.85 × 10^-13 F·m) / (0.01 m) = 8.85 × 10^-10 F.
- Step 7: Write the final answer: The capacitance of the capacitor is 8.85 × 10^-10 F.
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