Solve the Problem $\mathrm { q }$ (In Coulombs) Delivered by a Current

question 103

Multiple Choice

Solve the problem.
-The charge $\mathrm { q }$ (in coulombs) delivered by a current $\mathrm { i }$ (in amperes) is given by $\mathrm { q } = \int \mathrm { i } \mathrm { dt }$ , where $t$ is the time (in seconds) . A damped-out periodic wave form has current given by $\mathrm { i } = \mathrm { e } ^ { - 3 \mathrm { t } } \cos 5 \mathrm { t }$ . Find a formula for the charge delivered over time $t$ .

• A) \(\frac { e ^ { - 3 t } ( - 3 \cos 5 t + 5 \sin 5 t ) } { 25 } + C\)
• B) \(\frac { e ^ { - 3 t } ( - 3 \cos 5 t + \sin 5 ) } { 34 } + C\)
• C) \(\frac { e ^ { - 3 t } ( - 3 \cos 5 t + 5 \sin 5 t ) } { 34 } + C\)
• D) \(\frac { - 3 \cos 5 t + 5 \sin 5 t } { 34 } + C\)

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Definitions:

Coefficient of Correlation

A numerical measure that captures the direction and degree of a linear relationship between two variables.

Relationship

A connection, association, or involvement between two or more individuals, which can be social, romantic, professional, or familial.

Falsifiability

A principle that for a theory to be considered scientific, it must be able to be proven false under potential observations or experiments.

Hypothesis

A proposed explanation made on the basis of limited evidence as a starting point for further investigation.