When the key K is pressed at time t = 0, then which of the following statements about the current i in the resistor, AB of the given circuit [Fig] is true

Initially the current will pass through resistance between  AB and capacitor C. The current will not pass through the resistance which is in parallel to C. The only resistance in the circuit $={\mathrm{R}}_{\mathrm{AB}}=1000\mathrm{\Omega }$
$\begin{array}{r}\therefore \text{ Current }=\frac{2\mathrm{V}}{1000\mathrm{\Omega }}\\ =2\times {10}^{-3}\mathrm{amp}=2\mathrm{mA}\end{array}$
The charging of capacitor takes place. Soon after the capacitor is fully charged, no current will flow through C. The current will now flow through 1000$\mathrm{\Omega }$ across C. Total
resistance of the circuit will be 1000 + 1000 =2000 $\mathrm{\Omega }$
Current $=\frac{2\mathrm{V}}{2000\mathrm{\Omega }}=1\times {10}^{-3}\mathrm{amp}=1\mathrm{mA}$