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The circuit has initially no current. The switch is closed at t = 0.

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a

The current through the battery as a function of time is $i_{0} = 16 - 16 e^{- 5 t}$

b

The current through the 15H inductor is $i_{2} = 24 (1 - e^{- 5 t})$

c

The potential difference across the 3H inductor is $120 e^{- 5 t}$

d

The current through the 3H inductor is $24 (1 - e^{- 5 t})$

answer is A, C, D.

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Detailed Solution

Question Image
$i_{0} = 16 - 16 e^{- 5 t}$
For parallel combinations,
$3 \frac{d i_{i}}{d t} + 6 \frac{d i_{2}}{d t} = 6 \frac{d i_{i}}{d t} + 15 \frac{d i_{2}}{d t} \frac{d i_{i}}{d t} = - 3 \frac{d i_{2}}{d t} i_{0} = i_{1} + i_{2} \frac{d i_{0}}{d t} = \frac{d i_{1}}{d t} + \frac{d i_{2}}{d t} 80 e^{- 5 t} = - 2 \frac{d i_{2}}{d t} i_{2} = 8 (e^{- 5 t} - 1)$

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