RC charging circuit

Relevant wiki: RC Circuits (Direct Current)

The equation for the charge on the capacitor in and RC circuit is

$q = q_{max}(1-e^{\frac{-t}{\tau}}).$

Given $t = 15 \ln10 \text{ s}$ , calculate

$q_{max} = \varepsilon C = (4 \text{V})(5 \text{F}) = 20 \text{C}$

and

$\tau = RC = (3 \Omega)(5 \text{F}) = 15 \text{s}.$

Hence,

$q = q_{max}(1-e^{\frac{-t}{\tau}}) = 20(1-e^\frac{-15 \ln10}{15}) = 20(1-e^{-\ln10}) = 20(1-0.1) = 18 \text{C}.$