A Series Circuit Consists of a Resistor $R = 24 \Omega$

Multiple Choice

A series circuit consists of a resistor $R = 24 \Omega$ , an inductor with $L = 2 H$ , a capacitor with $C = 0.005 \mathrm {~F}$ , and a generator producing a voltage of $E ( t ) = 12 \cos ( 10 t )$ . If the initial charge is $Q = 0.001 \mathrm { C }$ and the initial current is 0 , find the charge $Q ( t )$ at time $t$ .

A) $Q ( t ) = e ^ { - 6 t } ( \cos ( 6 t ) - 0.06175 \sin ( 6 t ) )$
B) $Q ( t ) = e ^ { - 2 t } ( 0.051 \cos ( 2 t ) - 0.06175 \sin ( 2 t ) ) + \frac { 1 } { 20 } \sin ( 10 t )$
C) $Q ( t ) = e ^ { - 6 t } ( 0.001 \cos ( 8 t ) - 0.06175 \sin ( 8 t ) ) + \frac { 1 } { 20 } \sin ( 10 t )$
D) $Q ( t ) = e ^ { - 6 t } ( 0.001 \cos ( 8 t ) - 0.06175 \sin ( 8 t ) )$
E) $Q ( t ) = e ^ { - 3 t } ( \cos ( 5 t ) - 0.06175 \sin ( 5 t ) )$