The figure above shows a circuit containing an electromotive force (a battery), a capacitor with a capacitance of $C$ farads ${\rm (F)}$, and a resistor with a resistance of $R$ ohms ${\rm (\Omega) }$. The voltage drop across the capacitor is $Q/C$, where $Q$ is the charge (in coulombs), so in this case Kirchhoff's Law gives $$RI + \frac{Q}{C} = E(t) .$$ Since the current is $\displaystyle I = \frac{dQ}{dt}$, we have $$R \frac{dQ}{dt} + \frac{1}{C} Q = E(t).$$
Suppose the resistance is $20 \, {\rm \Omega}$, the capacitance is $0.05 {\rm F}$, a battery gives a constant voltage of $E(t)=30 {\rm V}$, and the initial charge is $Q(0)=0 {\rm C}$.
Find the charge and the current at time $t$.
$Q(t)=$ ,
$I(t)=$ .