Two capacitors of capacity `6 muF` and 3 muF` are charge `100 V` and `50 V` separately and connected as shown in Now all the three switches `S_(1),S_(2)`, and `S_(3)` are closed.

Which plates form an isolated system?

Options

A. Plate 1 and plate 4 separately
B. Plate 2 and plate 3 separately
C. Plate 1 and plate 4 jointly
D. Plate 2 and plate 3 jointly

Answer

D

Explanation

Plates 2 and 3 are joined together and they are neither connected to any of the terminals of the battery nor to any other source of charge. So, they jointly form an isolated system. Before closing the switches, charge are shown in Fig. After closing the switch let q charge goes from battery. Then charge on each will increase by q.
Applying Kirchhoff's voltage law, we get
`200-((600+q)/(6))-((150+q)/(3))=0`
or `q=100muC`
so charge on `6muF` capacitor will be `70muC` and `3muF` capacitor will be `250muC` from all the switches `100muC` of charge will flow.