The figure shows theree cirrcuit with idential batteries, inductors, and resistors. Rank the circuit according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first

Options

A. (i) `i_(2)gti_(3)gti_(1),(i_(1)=0)` (ii) `i_(2)gt i_(3) gt i_(1)`
B. (i) `i_(2) lt i_(3) lt i_(1),(i_(1)ne0)(ii)i_(2)gt i_(3)gti_(1)`
C. (ii) `i_(2)=i_(3)=i_(1), (i_(1)=0)` (ii) `i_(2)lti_(3)lti_(1)`
D. `(i)i_(2)=i_(3)gti_(1),(i_(1)ne0)` (ii) `i_(2)gti_(3)gti_(1)`

Answer

A

Explanation

(i) Just before closing the switch,

`i_(1)=0,i_(2)=(E)/(R),i_(3)=(E)/(2R)`
So, `i_(2)gti_(3)gti_(1)[i_(1)=0]`
(ii) After a long time closing the switch,

As, `i=(E)/(R)`
`rArr" "i_(1)=E//2R,i_(2)=2E//R,i_(3)=E//R`
Therefore, `i_(2)gti_(3)gti_(1)`.