For an infinite ladder network, adding one more repeating unit does not change the equivalent resistance ($R_{eq}$). Assuming the standard configuration for this result (series resistors $R_1 = 2\ \Omega$, parallel resistors $R_2 = 1\ \Omega$), the equation is $R_{eq} = R_1 + \frac{R_{eq}R_2}{R_{eq} + R_2}$. Substituting values: $R_{eq} = 2 + \frac{R_{eq}}{R_{eq} + 1}$. Solving the quadratic $R_{eq}^2 - 2R_{eq} - 2 = 0$ yields $R_{eq} = 1 + \sqrt{3} \approx 2.73\ \Omega$. The total resistance is $R_{total} = R_{eq} + r = 2.73 + 0.5 = 3.23\ \Omega$. The current $I = \frac{V}{R_{total}} = \frac{12\text{ V}}{3.23\ \Omega} \approx 3.72\text{ A}$ , .