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In the ciruit shown in figured C(1) =2C(...

In the ciruit shown in figured `C_(1) =2C_(2)`. Switch`S` is closed at timt `t =0`.Let `i_(1)` and `i_(2)` be currents flowing through `C_(1)` and `C_(2)` at any time `t`, then the ratio`i_(1)//i_(2)`

A

is constant

B

increases with increases in time `t`

C

decreases with increase in time `t`

D

first increases then decreases

Text Solution

Verified by Experts

The correct Answer is:
B
`i_(1) = (V)/(R ) e^((t)/(RC_(1))) & i_(2) = (V)/(R ) e^((t)/(RC_(2)))`
`(i_(1))/(i_(2)) = e^(-t//RC_(1))/e^(-t//RC_(2)) rArr(i_(1))/(i_(2)) = e^((t)/(RC_(2)))-(t)/(RC_(1))`

Putting `C_(1) = 2C_(2) rArr (i_(1))/(i_(2)) = e^((t)/(2RC_(2)))`
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