3capacitors of capacitances 2 microfarad ,3 microfarad and 6 microfrarad are connected in series with a 12 V battery .all the connecting wires are disconnected .the 3 positiveplates are connected together and the 3 negative plates are connected together.find the charges on the 3 capacitors after the recnnection

Asked by Subhashree Lenka | 16th May, 2015, 01:18: PM

Expert Answer:

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 style

The charge supplied by the battery of 12 V = q × V

                                                             = 1 μF × 12 V = 12 μC

Since 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 style

The 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)V

Q2 = (3μF)V

Q3 = (6μF)V

Substituting 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 style

we 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

Answered by Yashvanti Jain | 13th Dec, 2017, 06:38: PM