A parallel plate capacitor separated by an air gap is made of 0.8 m2 tin plates and 20 mm

Source: JAMB · 2023

A parallel plate capacitor separated by an air gap is made of 0.8 m2 tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate? [Take εo = 8.85 x 10-12 Fm-1]

A parallel plate capacitor separated by an air gap is made of 0.8 m2 tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate? [Take εo = 8.85 x 10-12 Fm-1]

  1. 35.4 nC
  2. 3.54 nC
  3. 4.25 nC
  4. 42.5 nC ✓
Explanation

For a parallel plate capacitor, C = ε₀A/d. Here d = 20 mm = 0.02 m.

C = (8.85 × 10⁻¹² × 0.8)/0.02 = 3.54 × 10⁻¹⁰ F.

Charge Q = CV = 3.54 × 10⁻¹⁰ × 120 = 4.25 × 10⁻⁸ C = 42.5 nC. The 3.54 nC option comes from forgetting to multiply by 120 V correctly or using the wrong power of ten.

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