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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

A rectangular dielectric slab has dimensions of 20 cm × 20 cm × 1.0...

A rectangular dielectric slab has dimensions of 20 cm×20 cm×1.0 mm20 \text{ cm} \times 20 \text{ cm} \times 1.0 \text{ mm} and a dielectric constant of 4.04.0. If its two square faces are metal-coated, determine the capacitance between these coated surfaces.

Options

  1. A0.35 nF0.35 \text{ nF}
  2. B7.08 nF7.08 \text{ nF}
  3. C1.42 nF1.42 \text{ nF}
  4. D0.14 nF0.14 \text{ nF}

Correct answer

C. 1.42 nF1.42 \text{ nF}

Step-by-step solution

The capacitance of a parallel plate capacitor with a dielectric is given by C=Kε0AdC = \dfrac{K \varepsilon_0 A}{d}

Given:
Dielectric constant, K=4.0K = 4.0
Area of the square faces, A=20 cm×20 cm=400 cm2=4×10−2 m2A = 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2 = 4 \times 10^{-2} \text{ m}^2
Distance between the plates (thickness), d=1.0 mm=10−3 md = 1.0 \text{ mm} = 10^{-3} \text{ m}
Permittivity of free space, ε0=8.85×10−12 F/m\varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m}

Substituting the values into the formula:
C=4.0×8.85×10−12×4×10−210−3C = \dfrac{4.0 \times 8.85 \times 10^{-12} \times 4 \times 10^{-2}}{10^{-3}}

C=141.6×10−11 FC = 141.6 \times 10^{-11} \text{ F}

C=1.416×10−9 F≈1.42 nFC = 1.416 \times 10^{-9} \text{ F} \approx 1.42 \text{ nF}
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