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12th Class Physics Electrostatics & Capacitance Question Bank MCQ - Electrostatic Potential and Capacitance

  • question_answer
    In a parallel plate capacitor of capacitance C, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is half of the separation between the plates. The capacitance will be:

    A) \[\frac{C}{2}\]                          

    B) 2C

    C) \[\frac{3C}{8}\]                        

    D) \[\frac{4C}{5}\]

    Correct Answer: B

    Solution :

    (b) 2C Before the metal sheet is inserted,\[C=\frac{{{\varepsilon }_{0}}A}{d}\] After the sheet is inserted, the system is equivalent to two capacitors in series, each of capacitance \[C'=\frac{{{\varepsilon }_{0}}A}{\left( d/4 \right)}=\frac{4{{\varepsilon }_{0}}A}{d}=4C\] Equivalent capacitance \[\frac{1}{{{C}_{eq}}}=\frac{1}{4C}+\frac{1}{4C}=\frac{2}{4C}\] \[{{C}_{eq}}=\frac{4C}{2}=2C\]


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