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JEE Main & Advanced JEE Main Paper Phase-I (Held on 08-1-2020 Morning)

  • question_answer
    Effective capacitance of parallel combination of two capacitors \[{{C}_{1}}\]and \[{{C}_{2}}\]is\[10\mu F\]. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor \[{{C}_{2}}\]is 4 times that of\[{{C}_{1}}\]. If these capacitors are connected in series, their effective capacitance will be: [JEE MAIN Held On 08-01-2020 Morning]

    A) 1.6 \[\mu F\]

    B) 3.2 \[\mu F\]

    C) 4.2 \[\mu F\]

    D) 8.4 \[\mu F\]

    Correct Answer: A

    Solution :

    [a] In parallel combination, \[{{C}_{1}}+{{C}_{2}}=10\mu F\] When connected across 1 V battery, then \[\frac{{{U}_{1}}}{{{U}_{2}}}=\frac{1}{4}\Rightarrow \frac{{{C}_{1}}}{{{C}_{2}}}=\frac{1}{4}\] \[\therefore {{C}_{2}}=8\mu F\]             \[{{C}_{1}}=2\mu F\] \[\therefore \] In series combination, \[{{C}_{equivalent}}=\frac{{{C}_{1}}{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}=\frac{16}{10}=1.6\mu F\]


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