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$$ $$ 8. $(1 \mathrm{pt})$ The figure above shows a circuit containing an electromotive force, a capacitor with a capacitance of $c$ farads (F), and a resistor with a resistance of sR$ ohms $\Omega$. The voltage drop across the capacitor is $Q / Cs, where $0$ is the charge (in coulombs), so in this case Kirchhoff's Law gives R I+\frac{QHC)=E(t) Generated by @WebWork, http://webwork.maa.org, Mathematical Association of AmericaSince $1=\frac{d QHcd t}$, we have $$ R \frac{d QHd t}+\frac{1}{C} Q=E(t) $$ Suppose the resistance is $20 Omegas, the capacitance is $0.1 \mathrm{-F1$, a battery gives a constant voltage of $50 \mathrm{-V]$, and the initial charge is $0(0)=0 \mathrm{C}$. Find the charge and the current at time $t$. $Q(t)=$ $I(t)=$CS.SD. 1781