A source of constant voltage \( V \) is connected to a resistance \( R \) and two ideal inductors \( L_{1} \) and \( L_{2} \) through a switch \( S \) as shown. There is no mutual inductance between the two inductors. The switch \( S \) is initially open. At \( t=0 \), the switch is closed and current begins to flow. Which of the following options is/are correct?
(1) The ratio of the currents through \( L_{1} \) and \( L_{2} \) is fixed at all times \( (t0) \)
(2) After a long time, the current through \( L_{1} \) will be \( \frac{V}{R} \frac{L_{2}}{L_{1}+L_{2}} \)
(3) After a long time, the current through \( L_{2} \) will be \( \frac{V}{R} \frac{L_{1}}{L_{1}+L_{2}} \)
(4) At \( t=0 \), the current through the resistance \( R \) is \( \frac{V}{R} \)
(JEE Advanced 2017)
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