\(\therefore\) Current through battery \(=\frac{V}{R_{2}}\)
At \(t=\infty\)
effective resistance, \(R_{e f f}=\frac{R_{1} R_{2}}{R_{1}+R_{2}}\)
\(\therefore \) Current through battery \(=\frac{V}{R_{e f f}}=\frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}}\)