2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Electrostatics & Capacitance

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

  • question_answer
    Two capacitors \[{{C}_{1}}=2\mu \,F\] and \[{{C}_{2}}\,=\,6\,\mu \,F\] in series, are connected in parallel to a third capacitor \[{{C}_{3}}=\,4\,\mu \,F\]. This arrangement is then connected to a battery of e.m.f. = 2V, as shown in the figure. How much energy is lost by the battery in charging the capacitors                              [MP PET 2001]

    A)            \[22\times {{10}^{-6}}\,J\]

    B)            \[11\times {{10}^{-6}}\,J\]

    C)            \[\left( \frac{32}{3} \right)\times {{10}^{-6}}\,J\]

    D)            \[\left( \frac{16}{3} \right)\times {{10}^{-6}}\,J\]

    Correct Answer: B

    Solution :

               \[{{C}_{eq}}=\frac{{{C}_{1}}{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}+{{C}_{3}}=\frac{2\times 6}{2+6}+4=5.5\,\mu \,F\]           Energy supplied \[(E)=QV=C{{V}^{2}}=22\times {{10}^{-6}}\,J\]                    P.E. stored\[(U)=\frac{1}{2}{{C}_{eq}}{{V}^{2}}=\frac{1}{2}\times 5.5\times {{(2)}^{2}}=11\times {{10}^{-6}}J\]                    Þ Energy lost\[=E-U=11\times {{10}^{-6}}\,J\]


You need to login to perform this action.
You will be redirected in 3 sec spinner