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    Question

    A parallel plate capacitor is half-filled with a

    dielectric slab (K = 4). What is its effective capacitance, assuming plate separation d?
    A (8ε0A) / (5d) Correct Answer Incorrect Answer
    B (4ε0A) / (5d) Correct Answer Incorrect Answer
    C (8ε0A) / (7d) Correct Answer Incorrect Answer
    D (4ε0A) / (d) Correct Answer Incorrect Answer

    Solution

    Let the parallel plate capacitor have plates of area A and separation d. The original capacitance without the dielectric is When a dielectric slab of thickness d/2 and dielectric constant K=4 is inserted, the capacitor can be considered as two capacitors connected in series: 1.     A capacitor with air (or vacuum, K=1) and plate separation d/2. Its capacitance 2.  A capacitor with the dielectric (K=4) and plate separation d/2. Its capacitance The effective capacitance Ceff of two capacitors in series is given by: Therefore the correct answer is option (A).

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