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

question 156

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) \(Q ( t ) = e ^ { - 3 t } ( \cos ( 5 t ) - 0.06175 \sin ( 5 t ) )\)

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Definitions:

Labor

Refers to human effort, both physical and mental, used in the production of goods and services.

Output

Output is the quantity of goods or services produced by a company, industry, or economy within a specified period.

Average Product

The output per unit of input, calculated by dividing total output by the quantity of inputs.

Law of Diminishing Returns

An economic principle stating that as additional units of a factor of production are added to a fixed amount of another factor, the incremental increase in output will eventually decrease.