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_(2) gt i_(3) gt i_(1)`
B. `i_(2) gt i_(1) gt i_(3)`
C. `i_(1) gt i_(2) gt i_(3)`
D. `i_(1) gt i_(3) gt i_(2)`

Answer

A

Explanation

In circuit (1), on closing the switch, the current in the inductor is zero due to self induction, i.e., `i_(1) = 0`.
In circuit (2), on closing the switch the current in the inductor is zero due to self induction.

Therefore,
`i_(2) = i' = (E)/(R_(1))`
In circuit (3), on closing the switch, the current in the inductor is again zero due to the same reason.

Therefore,
`i_(#) = i' = (E)/(R_(1) + R_(2))`
Thus, it is obvious that,
`i_(2) gt i_(3) gt i_(1) (=0)`