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

Answer 1

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

            $CV = CV_a + C_u * V_a$

=>          $C_u * V_a = CV - CV_a$

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

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

=>        $C_u = 5 *10^{-6} F$