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(A) Just after the switch is closed,the inductor acts as an open circuit (infinite resistance) because it opposes any change in current ($I = 0$ throu

Vedclass · Accepted Answer

$I_2 > I_3 > I_1$

Vedclass · Answer

(A) Just after the switch is closed,the inductor acts as an open circuit (infinite resistance) because it opposes any change in current ($I = 0$ through the inductor branch).For circuit $1$: The inductor is in series with the battery. Thus,the current $I_1 = 0$.For circuit $2$: The resistor is in parallel with the series combination of the inductor and another resistor. The inductor branch has infinite resistance,so the current flows only through the parallel resistor. Thus,$I_2 = \frac{\varepsilon}{R}$.For circuit $3$: The inductor is in parallel with a resistor. The inductor branch acts as an open circuit. The battery sees two resistors in series (the one in the main branch and the one in parallel). Thus,$I_3 = \frac{\varepsilon}{2R}$.Comparing the currents: $I_2 = \frac{\varepsilon}{R}$,$I_3 = \frac{\varepsilon}{2R}$,and $I_1 = 0$.Therefore,the ranking is $I_2 > I_3 > I_1$.

The figure shows three circuits with identical batteries,inductors,and resistors. Rank the circuits according to the currents through the battery just after the switch is closed,greatest first.

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