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 $12 - \mathrm { V }$ 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)
$I ( t ) = 0.742 e ^ { - 8 t }$

Question

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 $12 - \mathrm { V }$ 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) 
$I ( t ) = 0.742 e ^ { - 8 t }$

Quizplus · Accepted Answer

The circuit is an RLC circuit, and the current can be found using the differential equation for an RLC circuit with given initial conditions. The solution involves a damped sinusoidal function, which matches option B.

A Series Circuit Consists of a Resistor R=16ΩR = 16 \OmegaR=16Ω

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