An Electric Circuit Has an Inductance $L=0.5 \mathrm{H}$ , a Resistance $\mathrm{R}=1000 \Omega$

Multiple Choice

An electric circuit has an inductance $L=0.5 \mathrm{H}$ , a resistance $\mathrm{R}=1000 \Omega$ , and a capacitance $\mathrm{C}=1.0 \times$ $10^{-6} \mathrm{~F}$ . Find the equation for the current $\mathrm{i}$ if the voltage sourœ is $12 \mathrm{~V}$ .

A) $i=e^{1000 t}\left(k_{1} \sin 1000 t+k_{2} \cos 1000 t\right) +0.000012$
B) $i=e^{-1000 t}\left(k_{1} \sin 1000 t+k_{2} \cos 1000 t\right) +0.000012$
C) $i=e^{1000 t}\left(k_{1} \sin 1000 t+k_{2} \cos 1000 t\right)$
D) $i=e^{-1000 t}\left(k_{1} \sin 1000 t+k_{2} \cos 1000 t\right)$