Question

In the given circuit switch s is closed at t=0 after s is closed.

• A. Direction and mangitude of current in $4\Omega$ changes
  
• B. Time constant of circuit after closing switch is $\tau =8\mu s$
• C. Time constant of circuit after closing switch is $\tau =12\mu s$
• D. Current in $4\Omega$ becomes zero at any instant

Answer 1

Answer: (A), (B), (C)

The correct options are
A Direction and mangitude of current in $4\Omega$ changes

B Time constant of circuit after closing switch is $\tau =8\mu s$
C Time constant of circuit after closing switch is $\tau =12\mu s$


Before closing switch current in both resistance is i=2A clockwise After closing s,
$\Rightarrow$ By KVL,

$15-2i_1-\frac{q}{C}=0\&12=6i_1-4i_2$

at $t=0,q=0$
hence, $i_1=7.5A$
$\&i_2=-0.75A$

Time constant $\tau =C{R}_{eq}=6\mu F\times \frac{4}{3}\Omega =8\mu s$