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Q.

Consider the following circuit as shown below. The switch S is closed at t = 0 as shown in the figure. Then choose the correct statements :

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a

The current through $R_{1}$ just after closing of switch is 8A

b

The power supply by the battery as function of time is $36 (9 - e^{- 4 t})$

c

The current through $R_{2}$ after long time closing of switch is 3A

d

The current as function of time in the inductor is $3 (1 - e^{- 4 t}) A$

answer is A, C, D.

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Detailed Solution

Using Kirchhoff’s loop law
$- 3 i - 1 \frac{d i}{d t} - 3 i + 36 = 0$
$∴ \frac{d i}{d t} = 36 - 6 i$ ……….. (i)
$- 3 i - 6 (i - i_{1}) + 36 = 0$
$\Rightarrow 3 i - 2 i_{1} = 12$ ……….. (ii)
By (i) and (ii) $\frac{d i_{1}}{d t} = 12 - 4 i_{1}$
On solving
$i_{1} = 3 (1 - e^{- 4 t})$
From (ii) $i = 2 (1 - e^{- 4 t}) + 4$
Power supply by battery = $36 (2 i - i_{1}) = 36 (9 - e^{- 4 t})$

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Consider the following circuit as shown below. The switch S is closed at t = 0 as shown in the figure. Then choose the correct statements :