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Three capacitors of capacitances 2 micro Farad, 3 microfarad and 6 microfarad are connected in series with a 12 volt battery all the connecting wires are disconnected the three positive plates are connected together and the three negative plates are connected together.Find the charge on the three capacitors after the reconnection.

Three capacitors of capacitances 2 micro Farad, 3 microfarad and 6 microfarad are connected in series with a 12 volt battery all the connecting wires are disconnected the three positive plates are connected together and the three negative plates are connected together.Find the charge on the three capacitors after the reconnection.

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
The equivalent capacitance of the three capacitors in series is given as begin mathsize 12px style 1 over straight C space equals space fraction numerator 1 over denominator 2 μF end fraction space plus space fraction numerator 1 over denominator 3 μF end fraction space plus fraction numerator 1 over denominator 6 μF end fraction straight C space equals space 1 space μF end styleThe charge supplied by the battery of 12 V = q × V = 1 μF × 12 V = 12 μCSince the capacitors are then connected in series, 12 μC charge appears on each of the positive plates and -12μC charge on each of the negative plates.The capacitors are connected as shown below:The total capacitance is:begin mathsize 12px style straight Q subscript 1 space plus space straight Q subscript 2 space plus space straight Q subscript 3 space equals space 36 space μC end styleThe 36 μC charge is distributed as Q1, Q2 and Q3 on the three positive plates and –Q1, -Q2 and –Q3 on the negative plates.Also, the three positive terminals are now at the same common potential and the three negative plates are also at the same potential.Let the potential difference across each capacitor be V.Then,Q1 = (2μF)VQ2 = (3μF)VQ3 = (6μF)VSubstituting in the equation :begin mathsize 12px style straight Q subscript 1 space plus space straight Q subscript 2 space plus space straight Q subscript 3 space equals space 36 space μC end stylewe get:begin mathsize 12px style straight Q subscript 1 space equals space 72 over 11 μC space comma space straight Q subscript 2 space equals space 108 over 11 μC comma space space straight Q subscript 3 space equals space 216 over 11 μC end style

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