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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Grouping of Capacitors

  • question_answer
    A parallel plate capacitor with air as medium between the plates has a capacitance of \[10\mu F\]. The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant \[{{k}_{1}}=2\]and \[{{k}_{2}}=4\]. The capacitance of the system will now be [MP PMT 1987; RPET 2001]

    A)                    x\[10\mu F\]

    B)                    \[20\mu F\]

    C)                    \[30\mu F\]

    D)                    \[40\mu F\]

    Correct Answer: C

    Solution :

               \[{{C}_{R}}={{C}_{1}}+{{C}_{2}}=\frac{{{k}_{1}}{{\varepsilon }_{0}}{{A}_{1}}}{d}+\frac{{{k}_{2}}{{\varepsilon }_{0}}{{A}_{2}}}{d}\] \[=\frac{2\times {{\varepsilon }_{0}}\frac{A}{2}}{d}+\frac{4\times {{\varepsilon }_{0}}\frac{A}{2}}{d}\]\[=2\times \frac{10}{2}+4\times \frac{10}{2}=30\mu F\]


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