A 16.0 V parallel plate capacitor with square metal foils 10.0 cm long has a 0.002 – [Free] B54
A 16.0 V parallel plate capacitor with square metal foils 10.0 cm long has a 0.00250 mm thick mylay dielectric of constant 3.20. Calculate the capacitance.
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Answer
Capacitance of a Parallel-Plate Capacitor with Dielectric
🔹 Step 1: Given Parameters
- Voltage (V) = 16.0 V (not needed for this calculation)
- Plate Shape = Square
- Length of each plate side (L) = 10.0 cm = 0.100 m
- Dielectric thickness (d) = 0.00250 mm = 2.50 × 10⁻⁶ m
- Dielectric material = Mylar
- Dielectric constant (κ) = 3.20
- Vacuum permittivity (ε₀) = 8.854 × 10⁻¹² F/m
🔹 Step 2: Capacitance Formula
The capacitance of a parallel-plate capacitor with a dielectric is given by:
C = κ × ε₀ × (A / d)
Where:
- C = Capacitance
- κ = Dielectric constant
- ε₀ = Vacuum permittivity
- A = Area of plate
- d = Plate separation (dielectric thickness)
🔹 Step 3: Calculate Area of Square Plate
A = L² = (0.100)² = 0.0100 m²
🔹 Step 4: Substituting Values
C = (3.20)(8.854 × 10⁻¹²)(0.0100 / 2.50 × 10⁻⁶)
= (3.20)(8.854 × 10⁻¹²)(4.00 × 10³)
= 3.20 × 35.416 × 10⁻⁹
= 113.33 × 10⁻⁹ F
✅ Final Answer
Capacitance:
C = 113 nF