First slide

Inductance

Question

The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current (i₁ in circuit 1, i₂ in circuit 2, i₃ in circuit 3) through the battery (i) just after the switch is closed and (ii) a long time later, greatest first

Moderate

A

$(i) i_{2} > i_{3} > i_{1} (i_{1} = 0) (i i) i_{2} > i_{3} > i_{1}$
B

$(i) i_{2} < i_{3} < i_{1} (i_{1} \neq 0) (i i) i_{2} > i_{3} > i_{1}$
C

$(i) i_{2} > i_{3} = i_{1} (i_{1} = 0) (ii) i_{2} > i_{3} > i_{1}$
D

$(i) i_{2} = i_{3} > i_{1} (i_{1} \neq 0) (ii) i_{2} > i_{3} > i_{1}$

Solution

Just after closing the switch.
$i_{1} = 0, i_{2} = \frac{E}{R}, i_{3} = \frac{E}{2 R} so i_{2} > i_{3} > i_{1} (i_{1} = 0)$
After a long time closing the switch
$\begin{array}{l} Here i_{1} = \frac{ε}{2 R}, i_{2} = \frac{ε}{R / 2} and i_{3} = \frac{ε}{R} \\ Hence i_{2} > i_{3} > i_{1} \end{array}$

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