question_answer

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

A)  (i)\[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}({{i}_{1}}=0)\](ii) \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\]

B)  (i) \[{{i}_{2}}<{{i}_{3}}<{{i}_{1}}({{i}_{1}}\ne 0)\](ii)\[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\]

C)  (i) \[{{i}_{2}}={{i}_{3}}={{i}_{1}}({{i}_{1}}=0)\](ii)\[{{i}_{2}}<{{i}_{3}}<{{i}_{1}}\]

D)  (i) \[{{i}_{2}}={{i}_{3}}>{{i}_{1}}({{i}_{1}}\ne 0)\](ii)\[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\]

Correct Answer: A

Solution :

 Just before closing the switch: (i)f                                          (ii)                 (iii) \[{{i}_{1}}=0,{{i}_{2}}=\frac{E}{R},{{i}_{3}}=\frac{E}{2R}.\]So, \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}({{i}_{1}}=0)\]                 After a long time closing the switch:                 (i)                                                                            (ii)                                           (iii)                 Hence, \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}.\]