at instant $t$ - (here ammeter & voltmeter are ideal)
$C _{1}=40\, \mu F , R _{1}=25\, k \Omega$
$C _{2}=20\, \mu F , R _{2}=50\, k \Omega$
$i _{1}=\frac{ E }{ R _{1}} e ^{-\frac{t}{ R _{1} C _{1}}}$
i.e. $i _{1}=\left(0.2 e ^{-1}\right) m A$
$\& i _{2}=\left(0.1 e ^{-1}\right) m A$
$i = i _{1}+ i _{2}=\left(0.3 e ^{-t}\right) m A$
$i =0.3 e ^{-t} m A$
at $t =\infty, i =0$ i.e. option (D)
at $t =1,\,\, i =\frac{0.3}{ e }=\frac{ i _{0}}{ e }$ i.e. option (C)
at $t =0$ (just after key is pressed)- Reading of voltmeter
$V = V _{ N }- V _{ M }= V _{ B }- V _{ A }=-5$ volt
at $t =\ell n 2\, \sec$
$i _{1}=0.2 e ^{-\ln 2}$
$i _{1}=0.1\, mA$
and $i _{2}=0.05\, mA$
Apply KVL from $N \rightarrow M$ via cell
$V _{ N }+50 \times 0.05-5+25 \times 0.1- V _{ M }=0$
$V _{ N }- V _{ M }=0$
i.e. Reading of voltmeter is zero i.e. option (B) at $t =\infty, i =0$
hence reading of voltmeter, $V = V _{ N }- V _{ M }$
$V =5\, V$
