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In the given circuit (Fig), key K is swi...

In the given circuit (Fig), key `K` is switched on the at `t = 0`. The ratio of current `i` through the cell at `t = 0` to that at `t = oo` will be

A

`3 : 1`

B

`1 : 3`

C

`1 : 2`

D

`2 : 1`

Text Solution

Verified by Experts

At `t=0`, the branch containing `L` will offer infinite resistance while the branch containing the capacitor will be effectively a short circuit. Hence, `(R )_(L=0)=R` and `(i)_(t=0)=(epsilon)/(R )`. Similarly at `t=oo`, `L` will offer zero resistance whereas `c` will be an open circuit. Hence effective resistance `=R+(6xx3R)/(6+3)=3R` and `(i)_(t=oo)=(epsilon)/(3R)`
`:.` The required ratio `=(epsilon)/(R )xx(3R)/(epsilon)=3 : 1`
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