A Series Circuit Consists of a Resistor $R = 32 \Omega$

question 4

Multiple Choice

A series circuit consists of a resistor $R = 32 \Omega$ , an inductor with $L = 4 H$ , a capacitor with $C = 0.003125 \mathrm {~F}$ , and a $24$ -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

• A) \(I ( t ) = 0.742 e ^ { - 4 t } \sin ( 8 t )\)
• B) \(I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t )\)
• C) \(I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t ) - \frac { 1 } { 2 }\)
• D) \(I ( t ) = 0.742 e ^ { - 8 t }\)
• E) \(I ( t ) = \frac { e ^ { - 4 t } } { 160 } ( 0.003125 \cos ( 4 t ) + 8 \sin ( 4 t ) ) - \frac { 1 } { 2 }\)

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