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)gti_(3)gti_(1)`
B. `(i)i_(2)gti_(3)gti_(1)(i_(1)!=0)(ii)i_(2)gti_(3)gti_(1)`
C. `(i)i_(2)gti_(3)gti_(1)(i_(1)=0)(ii)i_(2)gti_(3)gti_(1)`
D. `(i)i_(2)gti_(3)gti_(1)(i_(1)!=0)(ii)i_(2)gti_(3)gti_(1)`

Answer

A

Explanation

At `t=0` , induced offers infinite resistance
At `t=prop` inductor offers zero resistance ltbr. `t=0` , `i_(1)=0` , `i_(2)=(E)/(2R)` , `i_(3)=(E)/(2R)`
`t=prop` , `i_(1)=(R)/(2R)` , `i_(2)=(2E)/(R)` , `i_(3)=(E)/(R)`
`t=0` , `i_(2)gti_(3)gti_(1)(i_(1)=0)`
`t=prop` , `i_(2)gti_(3)gti_(1)`