A Series Circuit Consists of a Resistor $R = 16 \Omega$

A series circuit consists of a resistor $R = 16 \Omega$ , an inductor with $L = 2 H$ , a capacitor with $C = 0.006250 F$ , and a $12 - V$ battery. If the initial charge is $0.0008 \mathrm { C }$ and the initial current is 0 , find the current $I ( t )$ at time $t$ .

A) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } ( 0.006250 \cos ( 4 t ) + 8 \sin ( 4 t ) ) - \frac { 1 } { 2 }$
B) $I ( t ) = 0.742 e ^ { - 4 t } \sin ( 8 t )$
C) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t ) \frac { 1 } { 2 }$
D) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t )$
E) $I ( t ) = 0.742 e ^ { - 8 t }$

Correct Answer:

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