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In the figure shows, all the capacitors ...

In the figure shows, all the capacitors are initially uncharged.
Case I: only switch `S_1` is closed
Case II: only switch `S_2` is closed
Case III: both swithces are closed
Find the ratio of the total energy stored in the system of capacitors for the cases I, II, and III, respectively.

A

`1:2:3`

B

`5:7:9`

C

`6:8:9`

D

`9:7:6`

Text Solution

Verified by Experts

The correct Answer is:
C
Case I: `C_(eq)=2C,U_(1)=(1)/(2)2CE^(2)=CE^(2)`
Case II: `C_(eq)=(8C)/(3),U_(2)=(1)/(2)(8C)/(3)E^(2)=(4)/(3)CE^(2)`
Case III: The upper `2C` will be short-circuited.
`U_(3)=(1)/(2)CE^(2)+(1)/(2)2CE^(2)=(3)/(2)CE^(2)`
`U_(1):U_(2):U_(3)=6:8:9`
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