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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        An air filled parallel plate capacitor charged to potential\[{{V}_{1}}\]is connected to an uncharged identical parallel plate capacitor with dielectric constant K. The common potential is\[{{V}_{2}}\]. The value of K is

    A)  \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\]                          

    B)  \[\frac{{{V}_{1}}}{{{V}_{1}}-{{V}_{2}}}\]

    C)  \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}}\]                               

    D)  \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}}\]

    Correct Answer: C

    Solution :

                    Common potential \[=\frac{total\text{ }charge}{total\text{ }capacity}\] \[{{V}_{2}}=\frac{{{C}_{0}}{{V}_{1}}+0}{{{C}_{0}}+K{{C}_{0}}}=\frac{{{V}_{1}}}{1+K}\]                 \[1+K=\frac{{{V}_{1}}}{{{V}_{2}}}\]                 \[K=\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}}\]


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