A 30-microfarad capacitor is charged to 90 v and then connected across an initially un charged capacitor of unknown capacitanc c .if the fin

Question

A 30-microfarad capacitor is charged to 90 v and then connected across an initially un charged capacitor of unknown capacitanc c .if the final potintial difference across the 30- microfarad capacitor is 20 v sitemin c

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Sapo 3 years 2021-07-25T03:32:30+00:00 1 Answers 9 views 0

Answers ( )

  1. minhkhang
    0
    2021-07-25T03:34:29+00:00
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    Answer:

    The value  is   C_u = 5 *10^{-6} F

    Explanation:

    From the question we are told that

       The voltage of the capacitor is  V = 90 \ V

       The  capacitance of the capacitor is  C = 30 \ \mu F = 30 *10^{-6} \ F

       The  final voltage is  V_a = 20 \ V

    Since the capacitors are connected in parallel we have that

          Q_u = Q'_u + Q

    Where  Q_u is the charge of the known capacitor before it is connected to the known capacitor

         Q_u' is the charge of the known capacitor after it is connected

           Q is the charge of the unknown capacitor

    Also the potential across the two capacitors will be the same (except for a loss due heat (it been converted to heat ))

    So

                CV = CV_a + C_u * V_a

    =>           C_u * V_a = CV - CV_a

    =>           C_u = \frac{CV - CV_a }{ V_a }

    =>           C_u = \frac{ [30*10^{-6} *90] - [30*10^{-6} * 20] }{ 20 }

    =>         C_u = 5 *10^{-6} F

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