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

question 53

Multiple Choice

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) \(I ( t ) = 0.742 e ^ { - 8 t }\)

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Definitions:

Pareto Optimal

A situation where resources are distributed in such a way that improving the condition of one person necessitates disadvantaging at least another individual.

Perfect Competition

A theoretical market structure that includes a large number of small firms, freedom of entry and exit, homogeneity of products, and perfect information.

Goods Distribution

The process of making a product or service available for the consumer or business user who needs it, which can involve transportation, packaging, and delivery.

Efficient Allocations

An economic condition where resources are distributed in the most effective manner, allowing for the optimization of outputs from given inputs without waste.