capacitance

Question

A parallel plate capacitor has plates of area 0.02 m² separated by 1 mm in air. What is its capacitance? (ε₀ = 8.85 × 10⁻¹² F/m)

RankGuru · Accepted Answer

1. **Capacitance Formula**: For parallel plates, $C = \frac{\epsilon_0 A}{d}$.
2. **Data Transformation**:
   - Area $A = 0.02$ m$^2$.
   - Separation $d = 1 	ext{ mm} = 10^{-3}$ m.
   - Constant $\epsilon_0 = 8.85 	imes 10^{-12}$ F/m.
3. **Calculation**:
   - $C = \frac{8.85 	imes 10^{-12} 	imes 0.02}{10^{-3}}$
   - $C = 8.85 	imes 10^{-12} 	imes 20$
   - $C = 177 	imes 10^{-12} = 1.77 	imes 10^{-10} 	ext{ F}$.
4. **Result**: The capacitance is **$1.77 	imes 10^{-10}$ F**.

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